10.4171/OWR/2020/13).
|
S13. |
M. Kantner, T. Höhne, TH. Koprucki, S. Burger, H.-J. Wünsche,
F. Schmidt, A. Mielke, U. Bandelow:
Multi-dimensional modeling and simulation of semiconductor nanophotonic devices.
Chapter 7 in "M. Kneissl, A. Knorr, S. Reitzenstein, A. Hoffmann:
Semiconductor Nanophotonics: Materials, Models, and Devices.
Springer Series in Solid-State Sciences SSSOL 194, Springer 2020",
pages 241--283. (Links:
WIAS preprint 2575; DOI: 10.1007/978-3-030-35656-9_7)
|
|
2019
| |
|---|
|
J154. |
A. Bacho, E. Emmrich, A. Mielke: An existence result and evolutionary
Gamma-convergence for perturbed gradient systems.
J. Evol. Eqns. 19 (2019) 479-522. (Links:
WIAS preprint 2499 ; DOI:
10.1007/s00028-019-00484-x)
|
|
J153. |
P. Dondl, Th. Frenzel, A. Mielke:
A gradient system with a wiggly energy and relaxed EDP-convergence.
ESAIM COCV, 25 (2019), 68/1--68/45.
(Links:
WIAS preprint 2459; DOI: 10.1051/cocv/201805)
|
|
J152. |
V. Laschos, A. Mielke:
Geometric properties of cones with applications on the Hellinger-Kantorovich
space, and a new distance on the space of probability measures.
J. Funct. Anal. 276:11 (2019), 3529--3576.
(Links:
WIAS preprint 2458; DOI:
10.1016/j.jfa.2018.12.013)
|
|
S12. |
M. Kantner, A. Mielke, M. Mittnenzweig, N. Rotundo:
Mathematical modeling of semiconductors: from quantum mechanics to devices.
In "J.F. Rodrigues and M. Hintermüller (eds):
Topics in Applied Analysis and Optimisation.
CIM Series in Mathematical Sciences, Springer 2019, pages 269-293.
(Links:
WIAS preprint 2575; DOI:
10.1007/978-3-030-33116-0_11)
|
|
M14. |
E. Pipping: Existence of long-time solutions to dynamic problems of
viscoelasticity with rate-and-state friction. ZAMM - Z. angew. Math.
Mech. 99(11) 10 pp., 2019. (doi: 10.1002/zamm.201800263)
Open Access. (Before Elias Pipping passed away in October 1, 2017, he
entrusted A. Mielke to submit and publish his finished work on his behalf).
|
|
2018
| |
|---|
|
J151. |
O. Burylko, A. Mielke, M. Wolfrum, S. Yanchuk:
Coexistence of Hamiltonian-like and dissipative dynamics in chains
of coupled phase oscillators with skew-symmetric coupling.
SIAM J. Appl. Dyn. Systems, 17(3) 2076--2105, 2018, (DOI: 10.1137/17M1155685).
|
|
J150. |
M. Liero, A. Mielke, G. Savaré.
Optimal entropy-transport problems and a new Hellinger-Kantorovich distance
between positive measures. Inventiones mathematicae, 211(3)
969--1117, 2018, (DOI: 10.1007/s00222-017-0759-8).
Open Access .
|
|
J149. |
M. Becker, Th. Frenzel, Th. Niedemeyer, S. Reichelt, A. Mielke, M. Bär.
Local control of globally competing patterns in coupled Swift-Hohenberg equations.
Chaos, 28(4) 043121, 11 pp, 2018, (DOI: 10.1063/1.5018139).
|
|
J148. |
A. Mielke, M. Mittnenzweig.
Convergence to equilibrium in energy-reaction-diffusion systems using
vector-valued functional inequalities., J. Nonlin. Science, 28(2)
765--806, 2018, (DOI: 10.1007/s00332-017-9427-9).
|
|
J147. |
J. Haskovec, S. Hittmeir, P. Markowich, A. Mielke:
Decay to equilibrium for energy-reaction-diffusion systems,
SIAM J. Math. Analysis, 50(1) 1037-1075, 2018
(DOI: 10.1137/16M1062065).
|
|
J146. |
A. Mielke, R. Rossi, G. Savaré.
Global existence results for viscoplasticity at finite strain,
Archive Rat. Mech. Analysis, 227(1) 423-475, 2018
(DOI: 10.1007/s00205-017-1164-6).
|
|
P64. |
A. Mielke:
Global existence for finite-strain viscoplasticity.
Oberwolfach Reports, 15(1) 278-281, 2018
(DOI:
10.4171/owr/2017/5)
|
|
P63. |
A. Mielke:
Three examples concerning the interaction of dry friction and oscillations.
Springer INdAM Series "Trends on Applications of Mathematics to Mechanics"
(Springer Proceedings of the INdAM-ISIMM Workshop, Rome, Italy, September 2016),
27: 159-177, 2018, (DOI:10.1007/978-3-319-75940-1_8).
|
|
2017
| |
|---|
|
J145. |
A. Mielke and C. Patz.
Uniform asymptotic expansions for the infinite harmonic chain.
Zeitschrift f. Anal. und Anwend., 26(4) 437-475, 2017
(doi: 10.4171/ZAA/1596).
|
|
J144. |
Mielke, R. Patterson, M. Peletier, M. Renger.
Non-equilibrium thermodynamical principles for chemical reactions with mass-action kinetics.
SIAM J. Appl. Math., 77(4) 1562-1585, 2017 (doi:10.1137/16M1102240).
|
| J143.
|
M. Heida, A. Mielke:
Averaging of time-periodic dissipation potentials in rate-independent processes,
Discrete Contin. Dyn. Syst. Ser. S, 10(6) 1303-1327, 2017 (doi: 10.3934/dcdss.2017070).
|
|
J142. |
M. Mittnenzweig, A. Mielke:
An entropic gradient structure for Lindblad equations and
couplings of quantum systems to macroscopic models.
J. Stat. Physics 167(2) 205-233, 2017 (doi:10.1007/s10955-017-1756-4).
|
|
J141. |
M. Liero, A. Mielke, M. Peletier, D.R.M. Renger.
On
microscopic origins of generalized gradient structures.
Discrete Contin. Dyn. Syst. Ser. S 10(1) 1-35, 2017 (Proceedings of STAMM 2014 in Poitiers, doi: 10.3934/dcdss.2017001).
|
|
P62. |
A. Mielke, M. Peletier, D. Slepcev. Variational Methods for Evolution,
Oberwolfach Reports, 14(4) 3185-3261, 2017 (doi:10.4171/owr/2017/54)
|
|
P61. |
A. Mielke, D. Peschka, N. Rotundo, M. Thomas.
On some extension of energy-drift-diffusion models: Gradient structure
for optoelectronic models of semiconductors.
In "P. Quintela et al. (eds): Progress in Industrial Mathematics at ECMI 2016
Mathematics in Industry Vol. 26, Springer 2017", pages 291-298
(DOI:
10.1007/978-3-319-63082-3_45).
|
|
P60. |
A. Mielke:
Uniform exponential decay for reaction-diffusion systems with complex-balanced
mass-action kinetics.
In "P. Gurevich, J. Hell, B. Sandstede, A. Scheel (eds):
Pattern of Dynamics
(Proceedings of the International Conference on Patterns of Dynamics 2016)
Springer Proceedings in Mathematics & Statistics Vol. 205,
Springer 2017", pages 149-171.
( DOI:
10.1007/978-3-319-64173-7_10).
|
|
M13. |
H.-Chr. Kaiser, D. Knees, A. Mielke, J. Rehberg, E. Rocca, M. Thomas, E. Valdinoci.
"PDE 2015: Theory and Applications of Partial Differential Equations",
proceedings of PDE 2015,
DCDS-S Discrete Contin. Dyn. Syst. Ser. S, 10(4) pages i-iv + 933, 2017
(DOI:
10.3934/dcdss.201704i ).
|
|
2016
| |
|---|
|
J140. |
A. Mielke and T. Roubíček.
Rate-independent elastoplasticity at finite strain and its numerical
approximation. Math. Models Meth. Appl. Sciences
26(12) 2203-2236, 2016.
|
|
J139. |
M. Liero, A. Mielke, G. Savaré.
Optimal transport in competition with reaction: The Hellinger-Kantorovich distance and geodesic curves.
SIAM J. Math Analysis, 18: 2869-2911, 2016.
|
|
J138. |
A. Mielke, R. Rossi, G. Savaré.
Balanced viscosity (BV) solutions to infinite-dimensional rate-independent systems.
J. Eur. Math. Soc. (JEMS), 18: 2107-2165, 2016.
|
|
J137. |
A. Mielke, M. Peletier, D.R.M. Renger.
A generalization of Onsager's reciprocity relations to gradient
flows with nonlinear mobility.
J. Non-Equilib. Thermodyn., 41(2) 141-149, 2016.
|
|
J136. |
S. Heinz, A. Mielke:
Existence, numerical convergence, and evolutionary relaxation for
a rate-independent phase-transformation model.
Phil. Trans. A, vol. 374, article 20150171 (23 pages) 2016.
|
|
S11. |
A. Mielke:
On evolutionary Γ-convergence for gradient systems.
In "A. Muntean, J. Rademacher, A. Zagaris (eds):
Macroscopic and Large Scale Phenomena:
Coarse Graining, Mean Field Limits and Ergodicity.
Proceedings of Summer School in Twente University (June 2012),
Lecture Notes in Appl. Math. Mech. Vol. 1, Springer 2016",
pages 187-249.
|
|
P59. |
A. Mielke:
Free energy, free entropy, and a gradient structure for thermoplasticity.
In "K. Weinberg and A. Pandolfi (eds): Innovative Numerical
Approaches for Multi-Field and Multi-Scale Problems.
Lecture Notes in Appl. Comp. Mechanics Vol. 81, Springer 2016",
pages 135-160.
|
|
P58. |
A. Mielke, R. Rossi, G. Savaré.
Balanced-Viscosity solutions for multi-rate systems.
J. Phys., MURPHYS-HSFS Proc., eds. O. Klein et al., vol. 727(1),
article 012010, 26 pages, 2016 (LINK:
pdf)
|
|
P57. |
A. Mielke:
Relaxation of a rate-independent phase-transformation model
for the evolution of microstructure
Oberwolfach Reports 13(1) 840-842, 2016.
(DOI:
10.4171/OWR/2016/17 )
|
|
P56. |
A. Mielke:
Deriving effective models for multiscale systems via
evolutionary Γ-convergence.
In "E. Schöll, S. Klapp,
Ph. Hövel (eds): Control of Self-Organizing Nonlinear Systems,
Springer 2016", pages 235-251.
|
|
2015
| |
|
B8. |
B. Fiedler, M. Haragus, A. Mielke, G. Raugel,
Y. Yi (editors). Special Issue in Memory of Klaus Kirchgässner.
J. Dynam. Differential Equations, Volume 27(3-4) 333-1171, 2015.
|
|
B7. |
A. Mielke, T. Roubíček.
Rate-Independent Systems: Theory and Application.
Applied Mathematical Sciences Vol. 193, XXII+660 pages,
New York: Springer 2015.
|
|
S10. |
A. Mielke:
Variational approaches and methods for dissipative material models
with multiple scales. Chapter 5 in "S. Conti, K. Hackl:
Analysis and Computation of Microstructure in Finite Plasticity,
Lecture Notes in Appl. Comp. Mechanics Vol. 78. Springer 2015".
pages 125-155.
|
| J135. |
A. Mielke, J. Haskovec, P. Markowich.
On uniform decay of the entropy for reaction-diffusion systems.
J. Dynam. Differential Equations, 27(3-4) 897-928, 2015.
|
|
J134. |
Dreyer, R. Huth, A. Mielke, J. Rehberg, M. Winkler.
Global existence for a nonlocal and nonlinear Fokker-Planck equation.
ZAMP, 66: 293-315, 2015.
|
|
J133. |
A. Mielke, J. Naumann.
Global-in-time existence of weak solutions to Kolmogorov's two-equation
model of turbulence. Comptes Rendus Acad. Sci. Paris Ser. I,
353: 321-326, 2015.
|
|
J132. |
A. Mielke:
Deriving amplitude equations via evolutionary Γ-convergence.
Discrete Contin. Dyn. Syst. Ser. A, 35(6) 2679-2700, 2015.
|
|
J130. |
S. Yanchuk, L. Lücken, M. Wolfrum, A. Mielke:
Spectrum and amplitude equations for scalar delay-differential equations
with large delay. Discrete Contin. Dyn. Syst. Ser. A,
35(1) 537-553, 2015.
|
|
P55. |
A. Mielke:
Evolutionary relaxation of a two-phase model.
Oberwolfach Reports 12(4) 3027-3030, 2015.
(DOI:
10.4171/OWR/2015/53 )
|
| P54. |
A. Mielke:
On thermodynamical couplings of quantum mechanics and macroscopic systems.
In "P. Exner, W. König, H. Neidhardt:
Mathematical Results in Quantum Mechanics (Proc. of QMath12 Conference)
World Scientific 2015", pages 331-348.
|
| M12. |
A. Mielke, G. Raugel, J. Scheurle.
In Memoriam Klaus Kirchgässner.
J. Dynam. Differential Equations, 27(3-4) 335-342, 2015.
|
|
2014
| |
|---|
| J131. |
A. Mielke, M.A. Peletier, D.R.M. Renger.
On the relation between gradient flows and the large-deviation principle,
with applications to Markov chains and diffusion.
Potential Analysis, 41(4) 1293-1327, 2014.
|
| J129. |
A. Mielke, S. Reichelt, M. Thomas.
Two-scale homogenization of nonlinear reaction-diffusion systems
with slow diffusion.
AIMS J. Networks and Heterogeneous Media, 9(2) 353-382, 2014.
|
| J128. |
A. Mielke and S. Zelik.
On the vanishing-viscosity limit in parabolic systems with
rate-independent dissipation terms.
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), XIII: 67-135, 2014.
|
| J127. |
A. Mielke, Ch. Ortner, Y. Şengül.
An approach to nonlinear viscoelasticity via metric gradient flow.
SIAM J. Math Analysis, 46(2) 1317-1347, 2014.
|
| P53. |
L. Ambrosio, A. Mielke, M.A. Peletier, G. Savaré.
Variational methods for evolution.
Oberwolfach Reports, 3177-3254, 2014.
|
| P52. |
A. Glitzky, A. Mielke, L. Recke, M. Wolfrum, S. Yanchuk.
D2 -- Mathematics for optoelectronic devices.
In "MATHEON -- Mathematics for Key Technologies."
EMS Series in Industrial and Applied Mathematics,
vol. 1(1) 243-256, 2014.
|
| P51. |
D. Knees, R. Kornhuber, Chr. Kraus, A. Mielke, J. Sprekels.
C3 -- Phase transformation and separation in solids.
In "MATHEON -- Mathematics for Key Technologies."
EMS Series in Industrial and Applied Mathematics,
vol. 1(1) 189-203, 2014.
|
| M11. |
V. Mehrmann, A. Mielke, F. Schmidt.
D -- Electronic and photonic devices.
In "MATHEON -- Mathematics for Key Technologies."
EMS Series in Industrial and Applied Mathematics,
vol. 1(1) 229-232, 2014.
|
|
2013
| |
|---|
| J126. |
M. Liero and A. Mielke: Gradient structures and geodesic convexity for reaction-diffusion systems. Phil. Trans. Royal Soc. A., 371(2005) 20120346 (28 pages), 2013.
|
| J125. |
A. Mielke: Geodesic convexity of the relative entropy in reversible Markov chains. Calc. Var. Part. Diff. Equ., 48(1) 1-31, 2013.
|
| J124. |
A. Mielke and U. Stefanelli. Linearized plasticity is the evolutionary Γ-limit of finite plasticity. J. Eur. Math. Soc. (JEMS), 15(3) 923-948, 2013.
|
| J123. |
A. Mielke and E. Rohan. Homogenization of elastic waves in fluid-saturated porous media using the Biot model. Math. Models Meth. Appl. Sci., 23(5) 873-916, 2013.
|
| J122. |
A. Glitzky and A. Mielke:
A gradient structure for systems coupling reaction-diffusion effects in bulk and interfaces. Z. angew. Math. Physik (ZAMP), 64(1) 29-52, 2013.
|
| J121. |
A. Mielke, R. Rossi and G. Savaré.
Nonsmooth analysis of doubly nonlinear evolution equations. Calc. Var. 46: 253-310, 2013.
|
| J120. |
A. Mielke: Thermomechanical modeling of energy-reaction-diffusion systems, including bulk-interface interactions. Discrete Contin. Dyn. Syst.-S, 6(2) 479-499, 2013.
|
| M10. |
A. Mielke: Luftballons im Handy-Akku. Die Welt, Eine Minute Mathematik, S. 22, 21.03.2013, English version.
|
| M9. |
G. Dal Maso, A. Mielke, and U. Stefanelli. Rate-independent Evolutions. (Editorial to Special Volume of 275 pp.) Discrete Contin. Dyn. Syst.-S, 6 (1) i--ii, 2013.
|
| S9. |
A. Mielke: Dissipative quantum mechanics using GENERIC, Proc. of the conference on Recent Trends in Dynamical Systems, vol. 35 of Proceedings in Mathematics & Statistics, Springer, 2013: 555-585.
|
| P50. |
A. Mielke:
Gradient structures and dissipation distances for
reaction-diffusion systems.
Oberwolfach Reports 10(4) 3455-3458, 2013.
(DOI:
10.4171/OWR/2013/59 )
|
| P49. |
U. Bandelow, Th. Koprucki, K. Gärtner, A. Wilms,
A. Mielke:
Comprehensive mathematical modeling and simulation of semiconductor lasers.
Proc. of iNOW 2013: pp. A7-A8, 2013.
|
|
2012
| |
|---|
| J119. |
A. Mielke, R. Rossi and G. Savaré. Variational convergence of gradient flows and rate-independent evolutions in metric spaces, Milan J. Math., 80: 381-410, 2012.
|
| J118. |
K. Hackl, S. Heinz, A. Mielke: A model for the evolution of laminates in finite-strain elastoplasticity. ZAMM Z. angew. Math. Mech., 92(11-12) 888-909, 2012.
|
| J117. |
A. Mielke: Emergence of rate-independent dissipation from viscous systems with wiggly energies. Contin. Mech. Thermodyn., 24(4) 591-603, 2012.
|
| J116. |
A. Mielke, T. Roubíček, and M. Thomas. From damage to delamination in nonlinearly elastic materials at small strains. J. Elasticity, 109: 235-273, 2012.
|
| J115. |
S. Amiranashvili, U. Bandelow and A. Mielke: Calculation of ultrashort pulse propagation based on rational approximations for medium dispersion. Opt. Quantum Electron., 44: 241-246, 2012.
|
| J114. |
S. Arnrich, A. Mielke, M.A. Peletier, G. Savaré, M. Veneroni. Passing to the limit in a Wasserstein gradient flow: From
diffusion to reaction. Calc. Var. Partial Differential Equations, 44: 419-454, 2012.
|
| J113. |
S. Bartels, A. Mielke, and T. Roubíček. Quasistatic small-strain plasticity in the limit of vanishing hardening and its numerical approximation. SIAM J. Numer. Anal., 50(2) 951-976, 2012.
|
| J112. |
A. Mielke: Generalized Prandtl-Ishlinskii operators arising
from homogenization and dimension reduction. Physica B, 407(9) 1330-1335, 2012.
|
| J111. |
A. Mielke, R. Rossi and G. Savaré. BV solutions and viscosity approximations of rate-independent systems.
ESAIM Control Optim. Calc. Var., 18: 36-80, 2012.
|
|
|
| J110. |
A. Mielke and L. Truskinovsky. From discrete visco-elasticity to continuum rate-independent plasticity: Rigorous results. Arch. Rational Mech. Anal., 203: 577-619, 2012.
|
| P48. |
A. Mielke: Multiscale gradient systems and their amplitude equations. Oberwolfach Reports, 9(4) 3588-3591, 2012.
|
| 2011 |
|
| B6. |
S. Bianchini, E.A. Carlen, A. Mielke, C. Villani. Nonlinear PDEs and Applications. C.I.M.E. Summer School, Cetraro, Italy 2008. Lecture Notes in Mathematics, vol. 2028, 240 pages. Eds.: L. Ambrosio, G. Savaré. Springer, Heidelberg, 2011, s. WIAS preprint 1454.
|
| J109. |
M. Liero and A. Mielke: An evolutionary elastoplastic plate model derived via Γ-convergence. Math. Models Meth. Appl. Sci., 21 (9) 1961-1986, 2011.
|
| J108. |
A. Mielke: Formulation of thermoelastic dissipative material behavior using GENERIC. Contin. Mech. Thermodyn., 23 (3) 233-256, 2011.
|
| J107. |
A. Mielke: A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems.
Nonlinearity, 24: 1329-1346, 2011.
|
| J106. |
A. Mielke: On thermodynamically consistent models and
gradient structures for thermoplasticity. GAMM Mitteilungen, 34 (1) 51-58, 2011.
|
| J105. |
A. Mielke and U. Stefanelli. Weighted energy-dissipation functionals for
gradient flows.
ESAIM Control Optim. Calc. Var., 17: 52-85, 2011.
|
| J104. |
A. Mielke: Complete-damage evolution
based on energies and stresses. Special Issue "Thermomechanics and Phase Change" of Discrete Cont. Dyn. Syst. Ser. S, 4: 423-439, 2011.
|
| S8. |
A. Mielke: Differential, energetic, and metric formulations
for rate-independent processes.
Chapter 3 in ``S. Bianchini, E.A. Carlen, A. Mielke, C. Villani: Nonlinear PDE's and Application, LNM 2028, Springer 2011'', pages 87-170.
|
| P47.
|
Editoren A. Mielke, F. Otto, G. Savar\'e, and U. Stefanelli. Variational Methods for Evolution. Oberwolfach Reports 8(4) 3145-3216, 2011.
|
| P46.
|
A. Mielke: Geometry and thermodynamics for the coupling of quantum mechanics and dissipative systems. Oberwolfach Reports 8(3) 2260-2263, 2011.
|
| 2010 |
|
| J103. |
J. Giannoulis, A. Mielke, and Chr. Sparber. High-frequency averaging in semi-classical Hartree-type equations.
Asymptot. Anal., 70: 87-100, 2010.
|
| J102. |
A. Mielke, L. Paoli, A. Petrov, and U. Stefanelli. Error
estimates for space-time discretizations of a rate-independent variational
inequality. SIAM J. Numer. Anal., 48(5) 1625-1646, 2010
|
| J101. |
A. Mielke, C. Patz.
Dispersive stability of infinite dimensional Hamiltonian systems on lattices.
Appl. Anal., 89(9) 1493-1512, 2010
|
| J100. |
D. Knees, C. Zanini, A. Mielke: Crack
growth in polyconvex materials. Physica D, 239 (2010) 1470-1484.
|
| J99. |
A. Mielke, T. Roubíček, and J. Zeman. Complete
damage in elastic and viscoelastic media and its energetics.
Comput. Methods Appl. Mech. Engrg. 199: 1242-1253, 2010.
|
| J98. |
M. Thomas, A. Mielke: Damage
of nonlinearly elastic materials at small strain - Existence and regularity results. ZAMM Z. angew. Math. Mech. 90(2) 88-112, 2010.
|
| J97. |
Sh. Amiranashvili, U. Bandelow, and A. Mielke: Padé approximant for
refractive index and nonlocal envelope equations. Opt. Commun., 283: 480-485, 2010.
|
| M8. |
A. Mielke: Mathematik für Nano- und Optoelektronik. Wissenschaft Berlin 2010, Kapitel "Mathematik und ihre Anwendungen", S. 118, Berliner Wirtschaftsgespräche.
|
| P45. |
A. Mielke On an evolutionary model for complete damage
based on energies and stresses.
Pubblicazione IMATI-CNR, T. Roubíček and U. Stefanelli, eds., 29PV10/27/0: 23-32, 2010.
|
| P44. |
A. Mielke, R. Rossi, and G. Savaré. A vanishing viscosity approach to rate-independent modeling in metric spaces.
Pubblicazione IMATI-CNR, T. Roubíček and U. Stefanelli, eds., 29PV10/27/0: 33-38, 2010.
|
| P43. |
A. Mielke and M. Ortiz. Microstructures in Solids: From Quantum Models to Continua,
Oberwolfach Reports, 7(1) 733-798, 2010.
|
| P41. |
A. Mielke, L. Paoli, A. Petrov, and U. Stefanelli. Error bounds for space-time discretizations of a
3D model for shape-memory materials, Proc. of the
IUTAM Symposium on Variational Concepts with Applications to the Mechanics of
Materials, K. Hackl, ed., vol. 21 of IUTAM Bookseries, Springer, 2010: 185-197.
|
| P40. |
Mielke: Existence theory for
finite-strain crystal plasticity with gradient regularization, Proc. of the
IUTAM Symposium on Variational Concepts with Applications to the Mechanics of
Materials, K. Hackl, ed., vol. 21 of IUTAM Bookseries, Springer, 2010: 171-183.
|
| 2009 |
|
| J96. |
A. Mielke, L. Paoli, A. Petrov. On existence and
approximation for a 3D model of thermally-induced phase transformations in
shape-memory alloys. SIAM J. Math. Anal., 41(4):
1388-1414, 2009.
|
| J95. |
A. Mielke, R. Rossi, G. Savaré. Modeling
solutions with jumps for rate-independent systems on metric
spaces. Discrete Contin. Dyn. Syst. Ser. A, 25(2) 585-615, 2009.
|
| J94. |
A. Mielke and T. Roubíček. Numerical
approaches to rate-independent processes and applications in
inelasticity. ESAIM Math. Mod. Num. Anal., 43: 399-428, 2009.
|
| J93. |
A. Mainik and A. Mielke: Global existence for rate-independent gradient plasticity at finite
strain. J. Nonlinear Sci., 19(3) 221-248, 2009.
|
| J92. |
A. Mielke and F. Rindler. Reverse
approximation of energetic solutions to rate-independent
processes. Nonl. diff. Eqns. Appl. (NoDEA)., 16(1) 17-40, 2009.
|
| J91. |
G. Bouchitté, A. Mielke, and
T. Roubíček. A complete-damage problem at small
strains. ZAMP Z. Angew. Math. Phys., 60: 205-236, 2009.
|
| J90. |
S. Zelik and A. Mielke: Multi-pulse evolution and
space-time chaos in dissipative systems. Mem. Amer. Math. Soc., 198
(925) 1-97, 2009.
|
| P42. |
A. Mielke: Vanishing-viscosity solutions for rate-independent systems,
Oberwolfach Reports, 6 (4) 3073-3076, 2009.
|
| P39. |
K. Hackl, S. Heinz and A. Mielke: A model for the evolution of laminates, PAMM 9(1), 2009: 43-46, published online, DOI: 10.1002/pamm.200910012.
|
| 2008 |
|
| M7. |
A. Mielke: Differential, energetic and
metric formulations for rate-independent processes, C.I.M.E. Summer School
on Nonlinear PDEs and Applications, Cetraro, June 2008.
|
| J89. |
A. Mielke and U. Stefanelli. A discrete variational principle
for rate-independent evolution. Advances in the Calculus of
Variations, vol. 1: 399-431, 2008.
|
| J88. |
J. Giannoulis, M. Herrmann, and A. Mielke: Lagrangian
and Hamiltonian two-scale reduction. J. Math. Phys., vol. 49, issue
10, 103505 (2008) 1-42.
|
| J87. |
D. Knees, A. Mielke, and C. Zanini. On
the inviscid limit of a model for crack propagation. Math. Models
Methods Appl. Sci., 18(9) 1529-1568, 2008.
|
| J86. |
A. Mielke, A. Petrov, J.A.C. Martins.
Convergence of solutions of kinetic variational inequalities in the
rate-independent quasi-static limit. J. Math. Anal. Appl., 348: 1012-1020, 2008.
|
| J85. |
D. Knees and A. Mielke: On the energy
release rate in finite-strain elasticity. Mechanics of
Adv. Mat. and Structures, 15: 421-427, 2008.
|
| J84. |
A. Mielke and M. Ortiz. A class
of minimum principles for characterizing the trajectories and the relaxation of
dissipative systems. ESAIM Control Optim. Calc. Var., 14: 494-516, 2008.
|
| J83. |
J. Giannoulis, A. Mielke, and C. Sparber. Interaction
of modulated pulses in the nonlinear Schrödinger equation with periodic
potential. J. Diff. Equ., 245: 939-963, 2008.
|
| J82. |
R. Rossi, A. Mielke, and G. Savaré. A
metric approach to a class of doubly nonlinear evolution equations and
applications. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5), vol. VII
(2008) 97-169.
|
| J80. |
D. Knees and A. Mielke: Energy
release rate for cracks in finite-strain elasticity. Math. Methods
Applied Sciences, 13(5)501-528, 2008.
|
| J79. |
A. Mielke, T. Roubíček, and U. Stefanelli.
Γ-limits and relaxations for rate-independent evolutionary
problems. Calc. Var. Part. Diff. Equ., 31: 387-416, 2008.
|
| J78. |
F. Auricchio, A. Mielke and U. Stefanelli. A
rate-independent model for the isothermal quasi-static evolution of
shape-memory materials. Math. Models Meth. Appl. Sci., 18(1) 125-164, 2008.
|
| J77. |
A. Mielke: Weak
convergence methods for Hamiltonian multiscale problems. DCDS(A)
Discrete Contin. Dyn. Syst. Ser. A, 20(1) 53-79, 2008.
|
| P38. |
A. Mielke: Lie groups in plasticity at finite strains. Oberwolfach Reports, 5(3) 1890-1893, 2008.
|
| P37. |
D. Knees, A. Mielke, and C. Zanini. On rate-independent models
for crack propagation. PAMM (Proceedings in
Applied Mathematics and Mechanics), 2008, 8 (1) 10213-10214.
|
| P36. |
A. Mielke, L. Paoli, and A. Petrov. Existence
and approximation for a 3D model of thermally-induced phase transformations in
shape-memory alloys. PAMM (Proceedings in
Applied Mathematics and Mechanics), 2008, 8 (1) 10395-10396.
|
| P35. |
A. Mielke: Numerical approximation techniques for rate-independent
inelasticity. Proc. of the IUTAM Symposium on Theoretical, Computational
and Modelling Aspects of Inelastic Media, B. D. Reddy, ed., vol. 11 of IUTAM
Bookseries, Springer, 2008: 53-63.
|
| P34. |
H. Gajewski, J. A. Griepentrog, A. Mielke, J. Beuthan, U. Zabarylo,
O. Minet.
Bildsegmentation
zur Untersuchung von Streulichtbildern bei der laseroptischen Diagnose von
rheumatoider Arthritis. In W. Jäger, H.-J. Krebs, editors,
Mathematics - Key Technology for the Future, english version "Image Segmentation for the
Investigation of Scattered-Light Images when Laser-Optically Diagnosing
Rheumatoid Arthritis": 149-161, Springer 2008.
|
| 2007 |
|
| J81. |
A. Mielke and A. Petrov. Thermally
driven phase transformation in shape-memory alloys.
Adv. Math. Sci. Appl, 17: 667-685, 2007.
|
| J76. |
A. Mielke: A
model for temperature-induced phase transformations in finite-strain
elasticity. IMA J. Appl. Math., 72(5) 644-658, 2007.
|
| J75. |
F. Schmid and A. Mielke: Existence
results for a contact problem with varying friction coefficient and nonlinear
forces. ZAMM Z. angew. Math. Mech., 87 (8-9) 616-631, 2007.
|
| J74. |
A. Mielke and A. Timofte. Two-scale
homogenization for evolutionary variational inequalities via the energetic
formulation. SIAM J. Math. Anal., 39 (2) 642-668, 2007.
|
| J73. |
A. Mielke and S.V. Zelik. Infinite-dimensional hyperbolic sets
and spatio-temporal chaos in reaction-diffusion systems in
Rn. J. Dynam. Differential Equations, 19(2) 333-389, 2007. |
| J72. |
A. Mielke and R. Rossi. Existence and uniqueness results for
a class of rate-independent hysteresis problems. Math. Models Methods
Appl. Sci., 17 (1) 81-123, 2007.
|
| M6. |
J. Cagnol, B. Miara, A. Mielke, and G. Stavroulakis.
State
of the Art, Trends, and Directions in Smart Systems. |
| M5. |
A. Mielke: Modeling
and analysis of rate-independent processes, Lipschitz Lectures, Universität Bonn, January 2007.
|
| P33. |
A. Mielke: Γ-convergence for rate-independent processes with
applications to damage. Oberwolfach
Reports, 4(2) 1617-1620, 2007.
|
| 2006 |
|
| B5. |
A. Mielke,
editor. Analysis, Modeling, and Simulation of Multiscale Problems (Final
Report of the DFG Priority Program SPP 1095), XVIII-697 pages.
© Springer,
September 2006. |
| B4. |
R. Helmig, A. Mielke, B. Wohlmuth,
editors. Multifield Problems in Fluid and Solid
Mechanics. Series Lecture Notes in Applied and Computational
Mechanics, 28, XI-571 pages. © Springer, August 2006.
|
| J71. |
A. Mielke and A. Timofte. Modeling and analytical study for ferroelectric
materials. Mechanics of Advanced Materials and Structures, 13: 457-462, 2006. |
| J70. |
M. Kočvara, A. Mielke, and
T. Roubíček. A rate-independent approach to the delamination
problem. Math. Mech. Solids, 11: 423-447, 2006.
|
| J69. |
A. Mielke: Macroscopic behavior of microscopic oscillations in harmonic lattices via
Wigner-Husimi transforms.
Arch. Rational Mech. Anal., 181: 401-448, 2006.
|
| J68. |
G. Francfort and A. Mielke: Existence results for a class of
rate-independent material models with nonconvex elastic energies. J. reine
angew. Math., 595: 55-91, 2006.
|
| J67. |
A. Mielke and A. Timofte. An energetic material model for
time-dependent ferroelectric behavior: existence and
uniqueness. Math. Meth. Appl. Sciences, 29: 1393-1410, 2006.
|
| J65. |
A. Mielke and T. Roubíček. Rate-independent damage
processes in nonlinear elasticity.
Math. Models Methods Appl. Sci., 16: 177-209, 2006. |
| J64. |
J. Giannoulis and A. Mielke: Dispersive evolution of pulses in
oscillator chains with general interaction
potentials. Discr. Cont. Dynam. Systems Ser. B, 6: 493-523, 2006. |
| J63. |
A. Mielke and S. Müller. Lower semicontinuity and existence
of minimizers for a functional in elastoplasticity. ZAMM
Z. angew. Math. Mech., 86: 233-250, 2006. |
| J62. |
M. Efendiev and A. Mielke: On the rate-independent limit of
systems with dry friction and small viscosity. J. Convex Analysis, 13: 151-167, 2006. |
| J61. |
W. Dreyer, M. Herrmann, and A. Mielke: Micro-macro transition
for the atomic chain via Whitham's modulation equation. Nonlinearity, 19: 471-500, 2006. |
| P31. |
A. Mielke: Deriving
modulation equations via Lagrangian and Hamiltonian reduction. Oberwolfach Reports,
3(4) 3032-3034, 2006. |
| P30. |
A. Mielke: Two-scale
modeling for Hamiltonian systems: formal and rigorous results.
Oberwolfach Reports, 3(4) 2656-2659, 2006. |
| P29. |
A. Mielke: Gamma
convergence for evolutionary problems. Oberwolfach Reports, 3(2) 1697-1700, 2006.
|
| P28. |
C. Patz, A. Mielke: Dispersive
and long-time behavior of oscillations in lattices. PAMM (Proceedings in
Applied Mathematics and Mechanics), DOI: 10.1002/pamm.200610232, pp.
503-504. Published
online. |
| P27. |
J. Giannoulis, M. Herrmann, and A. Mielke: Continuum descriptions for the
dynamics in discrete lattices: derivation and justification. In A. Mielke,
editor, Analysis, Modeling, and Simulation of Multiscale Problems: Final
report of the DFG Priority Program SPP 1095, pp. 435-466. Springer, 2006. |
| P26. |
E. Gürses, A. Mainik, C. Miehe, and A. Mielke: Analytical and numerical methods for
finite-strain elastoplasticity. In R. Helmig, A. Mielke, B. Wohlmuth,
editors, Multifield problems in Fluid and Solid
Mechanics. Series Lecture Notes in Applied and Computational
Mechanics, 28: 491-529. Springer, 2006. |
| P25. |
A. Mielke: A mathematical framework for standard generalized materials
in the rate-independent case. In R. Helmig, A. Mielke, B. Wohlmuth,
editors, Multifield problems in Fluid and Solid
Mechanics. Series Lecture Notes in Applied and Computational
Mechanics, 28: 399-428. Springer, 2006. |
| 2005 |
|
| J66. |
F. Schmid and A. Mielke: Vortex pinning in super-conductivity as
a rate-independent process. Europ. J. Appl. Math. 16: 799-808, 2005. Preprint (pdf). |
| J60. |
M. Kružík, A. Mielke, and
T. Roubíček. Modelling of microstructure and its evolution in
shape-memory-alloy single cristals, in particular in CuAlNi. Meccanica,
40: 389-418, 2005. |
| J59. |
A. Mielke: Necessary and sufficient conditions for polyconvexity
of isotropic functions. J. Convex Analysis, 12: 291-314, 2005. |
| J58. |
A. Afendikov and A. Mielke: Dynamical properties of spatially
non-decaying 2D Navier-Stokes flows with Kolmogorov forcing in an infinite
strip. J. Math. Fluid Mechanics, 7: S51-S67, 2005. |
| J57. |
A. Mainik and A. Mielke: Existence results for energetic models
for rate-independent systems. Calc. Var. PDEs, 22: 73-99, 2005. |
| S7. |
A. Mielke: Evolution in rate-independent systems (ch. 6). In
C. Dafermos and E. Feireisl, editors, Handbook of Differential Equations,
Evolutionary Equations, 2: 461-559. Elsevier B.V., 2005. |
| P24. |
A. Mielke: Some existence results in finite-strain
plasticity. Oberwolfach Reports, 2(4) 2991-2993, 2005. |
| P21. |
A. Mielke: Modeling and analysis of rate-independent processes in
continuum mechanics. In Y. Wang and K. Hutter, editors, Trends in
Applications of Mathematics to Mechanics, pp. 299-309. Shaker Verlag, 2005. |
| 2004 |
|
| J56. |
A. Mielke: Deriving new
evolution equations for microstructures via
relaxation of variational incremental problems. Comput. Methods
Appl. Mech. Engrg., 193: 5095-5127, 2004. |
| J55. |
A. Mielke: Existence of minimizers in incremental
elasto-plasticity with finite strains. SIAM J. Math. Analysis, 36: 384-404, 2004. |
| J54. |
A. Mielke and F. Theil. On rate-independent hysteresis
models. Nonl. diff. Eqns. Appl (NoDEA), 11: 151-189, 2004. |
| J53. |
Y.B. Fu and A. Mielke: Uniqueness of the surface-wave speed: a
proof that is independent of the Stroh formalism. Math. Mechanics
Solids, 9: 5-15, 2004. |
| J52. |
J. Giannoulis and A. Mielke: The nonlinear Schrödinger
equation as a macroscopic limit for an oscillator chain with cubic
nonlinearities. Nonlinearity, 17: 551-565, 2004. |
| J51. |
A. Mielke: Chaos and Šarkovskiís Anordnung der
natürlichen Zahlen. Mathematikinformation, 40: 48-54, 2004. |
| P23. |
A. Mielke: Energy transport in periodic lattices. Oberwolfach Reports, 1(4) 3019-3022, 2004. |
| P22. |
A. Mielke: Rate-independent models of phase transition. Oberwolfach Reports,
1(3) 1631-1634, 2004. |
| P20. |
J. Giannoulis and A. Mielke: Macroscopic pulse evolution for a
nonlinear oscillator chain. PAMM Proc. Appl. Math. Mech., 4: 540-541, 2004. |
| P19. |
A. Mielke: A new approach to elasto-plasticity using energy and
dissipation functionals. In J. Hill and R. Moore, editors, Applied
Mathematics Entering the 21st Century: Invited Talks from the ICIAM 2003
Congress, pp. 315-335. SIAM, 2004. |
| 2003 |
|
| J50. |
A. Mielke and T. Roubíček. A rate-independent model for
inelastic behavior of shape-memory alloys. Multiscale Model. Simul., 1: 571-597, 2003. |
| J49. |
A. Mielke: Energetic formulation of multiplicative
elasto-plasticity using dissipation
distances. Cont. Mech. Thermodynamics, 15: 351-382, 2003. |
| J48. |
T. Gallay and A. Mielke: Convergence results for a coarsening
model using global linearization. J. Nonlinear Science, 13: 311-346, 2003. |
| P18. |
K. Hackl, A. Mielke, and D. Mittenhuber. Dissipation distances
in multiplicative elastoplasticity. In W. Wendland and M. Efendiev, editors,
Analysis and Simulation of Multifield Problems, pp.
87-100. Springer-Verlag, 2003. |
| P17. |
A. Mielke: Evolution of rate-independent inelasticity with
microstructure using relaxation and Young measures. In C. Miehe, editor,
IUTAM Symposium on Computational Mechanics of Solid Materials at large Strains
(Stuttgart August 2001), pp. 33-44, Kluwer, 2003. |
| 2002 |
|
| J47. |
A. Mielke and S. Zelik. Infinite-dimensional trajectory
attractors for elliptic boundary-value problems on cylindrical
domains. Russian Math. Surveys, 57: 753-784, 2002. Translated in Uspekhi
Mat. Nauk, 57, no. 4(345) 119-150, 2002. |
| J46. |
A. Mielke: On the energetic stability of solitary water
waves. Phil. Trans. Royal Soc. London, 360: 2337-2358, 2002. |
| J45. |
Y.B. Fu and A. Mielke: A new identity for the surface impedance
matrix and its application to the determination of surface-wave speeds.
Proc. Royal Soc. London Ser. A, 458: 2523-2543, 2002. |
| J44. |
S. Govindjee, A. Mielke, and G. Hall. The free-energy of mixing
for n-variant martensitic phase transformations using quasi-convex
analysis. J. Mech. Physics Solids, 50: 1897-1922, 2002. Erratum and
Correct Reprinting: 51(4) 2003, pages 763 & I-XXVI. |
| J43. |
C. Carstensen, K. Hackl, and A. Mielke: Non-convex potentials
and microstructures in finite-strain plasticity. Proc. Royal Soc. London,
Ser. A, 458: 299-317, 2002. |
| J42. |
A. Mielke, F. Theil, and V.I. Levitas. A variational formulation
of rate-independent phase transformations using an extremum principle.
Arch. Rational Mech. Anal., 162: 137-177, 2002. Essential Science Indicator:
Emerging Research Fronts Paper in Mathematics in August 2006. |
| S6. |
A. Mielke: Analysis of energetic models for rate-independent
materials. In T. Li, editor, Proceedings of the Int. Congress of
Mathematicians 2002, Beijing, III: 817-828. Higher Education
Press, 2002. |
| S5. |
A. Mielke: Finite elastoplasticity, Lie groups and geodesics on
SL(d). In P. Newton, A. Weinstein, and P.J. Holmes, editors,
Geometry, Dynamics, and Mechanics, pp. 61-90. Springer-Verlag, 2002. |
| S4. |
A. Mielke: The Ginzburg-Landau equation in its role as a modulation
equation. In B. Fiedler, editor, Handbook of Dynamical Systems II, pp. 759-834. Elsevier Science B.V., 2002. |
| M4. |
A. Mielke: Relaxation via Young measures of material models for
rate-independent inelasticity. Stuttgart, 2002. |
| 2001 |
|
| J41. |
A. Afendikov and A. Mielke: Nonlocal modulation equations for
viscous fluid layer problems and persistence of spatially localized
pertrubations. Dokl. Akad. Nauk, 381(4) 479-483, 2001. Translated in
Doklady Physics 46(12) 869-872, 2001. |
| J40. |
B. Buffoni and A. Mielke: On interfaces between incompatible
wells and elastic deformations of infinite cylinders. Calc. Var. PDEs,
13: 469-489, 2001. |
| J39. |
A. Afendikov and A. Mielke: Multi-pulse solutions to the
Navier-Stokes problem between parallel plates. Z. angew. Math. Phys.,
52(1) 79-100, 2001. |
| J38. |
M. Groves and A. Mielke: A spatial dynamics approach to
three-dimensional gravity-capillary steady water waves.
Proc. Roy. Soc. Edinburgh Sect. A, 131: 83-136, 2001. Essential Science
Indicator:
Fast Breaking Paper in Mathematics in April 2003.
|
| S3. |
A. Mielke, G. Schneider, and H. Uecker. Stability and diffusive
dynamics on extended domains. In B. Fiedler, editor, Ergodic Theory,
Analysis, and Efficient Simulation of Dynamical Systems, pp. 563-583. Springer-Verlag, 2001. |
| 2000 |
|
| J37. |
A. Mielke, G. Schneider, and A. Ziegra. Comparison of inertial
manifolds and application to modulated systems. Math. Nachr., 214:
53-69, 2000. |
| J36. |
M.S. Kuczma and A. Mielke: Influence of hardening and
inhomogeneity on internal loops in pseudoelasticity. ZAMM
Z. Angew. Math. Mech., 80(5) 291-306, 2000. |
| S2. |
A. Mielke: Mathematical analysis of sideband instabilities with
application to Rayleigh-Bénard convection. In Mechanics: from theory
to computation, pp. 335-377. Springer, New York, 2000. |
| P16. |
A. Mielke: Estimates on the mixture function for multiphase
problems in elasticity. In A.-M. Sändig, W. Schiehlen, and W. Wendland,
editors, Multifield problems, pp. 96-103, Berlin, 2000. Springer-Verlag. |
| P15. |
A. Mielke: Exponentially weighed L∞-estimates and attractors for
parabolic systems on unbounded domains. In B. Fiedler, K. Gröger, and
J. Sprekels, editors, International Conference on Differential Equations
(Equadiff 99) Berlin 1999, vol. I, pp. 641-646. World Scientific, 2000. |
| P14. |
A. Mielke: Pattern formation on large domains and diffusive
mixing. In G. Iooss, O. Guès, and A. Nouri, editors, Trends in
applications of mathematics to mechanics (Nice, 1998), STAMM X, pp.
228-237. Chapman & Hall/CRC, Boca Raton, FL, 2000. |
| P13. |
A. Afendikov and A. Mielke: Multipulse solutions in problems
with reflection symmetry in cylindrical domains. In. B. Fiedler,
K. Gröger, and J. Sprekels, editors, International Conference on Differential Equations
(Equadiff 99) Berlin 1999, vol. I, pp. 769-771. World Scientific, 2000. |
| 1999 |
|
| J35. |
M.S. Kuczma, A. Mielke, and E. Stein. Modelling of hysteresis in
two-phase systems. Archive of Mechanics (Warzawa), 51: 693-715, 1999. |
|
J34. |
A. Afendikov and A. Mielke:
Bifurcation of homoclinic orbits to a saddle-focus in reversible
systems with SO(2) symmetry.
J. diff. Eqns, 159: 370-402, 1999.
|
|
J33. |
A. Afendikov and A. Mielke:
On families of reversible SO(2)-invariant vector fields with a non-semi-simple zero eigenvalue of
multiplicity four.
Dokl. Akad. Nauk, 369(2) 153-157, 1999. English
translation: Doklady Mathematics 60: 332-336, 1999.
|
|
J32. |
A. Mielke:
Flow properties for Young-measure solutions of semilinear hyperbolic problems.
Proc. Roy. Soc. Edinburgh Sect. A, 129: 85-123, 1999.
|
|
P12. |
A. Mielke and F. Theil.
A mathematical model for rate-independent phase transformations with hysteresis.
In H.-D. Alber, R. Balean, and R. Farwig, editors,
Proceedings of the Workshop on Models of
Continuum Mechanics in Analysis and Engineering,
pp. 117-129. Shaker-Verlag, 1999.
(Link to PDF)
|
|
1998
| |
|---|
|
J31. |
T. Gallay and A. Mielke:
Diffusive mixing of stable states in the Ginzburg-Landau equation.
Comm. Math. Phys., 199(1) 71-97, 1998.
|
| J30. |
A. Mielke, P.J. Holmes, and J.N. Kutz. Global existence and
uniqueness for an optical fibre laser model. Nonlinearity, 11: 1489-1504, 1998. |
| J29. |
A. Mielke and P. Sprenger. Quasiconvexity at the boundary and a
simple variational formulation of Agmon's condition. J. Elasticity, 51:
23-41, 1998. |
| J28. |
A. Mielke: Bounds for the solutions of the complex
Ginzburg-Landau equation in terms of the dispersion parameters. Phys. D,
117: 106-116, 1998. |
| M3. |
A. Mielke, F. Theil, and V.I. Levitas. Mathematical formulation
of quasistatic phase transformations with friction using an extremum
principle. Hannover, 1998. |
| 1997 |
|
| J27. |
A. Mielke: Instability and stability of rolls in the
Swift-Hohenberg equation. Comm. Math. Phys., 189: 829-853, 1997. |
| J26. |
A. Mielke:
The
complex Ginzburg-Landau equation on large and
unbounded domains: sharper bounds and attractors. Nonlinearity, 10: 199-222, 1997. |
| J25. |
A. Mielke: Mathematical analysis of sideband instabilities with
application to Reyleigh-Bénard convection. J. Nonlinear Sci., 7:
57-99, 1997. |
| P11. |
A. Mielke and P. Sprenger. Homogeneous deformations as global
minimizers in nonlinear elasticity. In ZAMM
Z. angew. Math. Mech. (Suppl. 2), 77: S683-684, 1997. |
| P10. |
M.S. Kuczma, V.I. Levitas, A. Mielke, and
E. Stein. Nonisothermal hysteresis loops in pseudoelasticity. In A. Garstecki
and J. Rakowski, editors, Proc. XIII Polish Conf. on Computer Methods in
Mechanics, Poznan, May 5-9, 1997, II: 711-718, 1997. |
| P9. |
M.S. Kuczma and A. Mielke: Variational approach to pseudoelastic
behaviour. In ZAMM Z. angew. Math. Mech. (Suppl. 1), 77: S176-177, 1997. |
| 1996 |
|
| B3. |
G. Dangelmayr, B. Fiedler, K. Kirchgässner, and A. Mielke,
editors. Dynamics of Nonlinear Waves in Dissipative Systems: Reduction,
Bifucation and Stability. Pitman Research Notes in Mathematics Series,
Vol. 352, 277 pages. Longman, Harlow, 1996. With contribution by G. Raugel. |
| S1. |
A. Mielke and G. Schneider. Derivation and justification of the
complext Ginzburg-Landau equation as a modulation equation. In. P. Deift,
C. Levermore, and C. Wayne, editors. Dynamical systems and probabilistic
methods in partial differential equations (Berkeley, CA, 1994), pp.
191-216. Amer. Math. Soc., Providence, RI, 1996. |
| J24. |
T. Bridges and A. Mielke: Instability of spatially-periodic
states for a family of semilinear PDE's on an infinite
strip. Math. Nachr., 179: 5-25, 1996. |
| 1995 |
|
| B2. |
A. Mielke and K. Kirchgässner, editors. Structure and Dynamics of
Nonlinear Waves in Fluids. Proceedings of the IUTAM/ISIMM Symposium held in
Hannover, August 17-20, 1994. World Scientific Publishing Co. Inc., Singapore, 1995. |
| J23. |
Th.J. Bridges and A. Mielke:
A proof of the Benjamin-Feir instability.
Arch. Rational Mech. Anal., 133: 145-198, 1995.
DOI:
10.1007/BF00376815
|
| J22. |
A. Mielke and G. Schneider. Attractors for modulation equations
on unbounded domains - existence and comparison. Nonlinearity, 8: 743-768, 1995. |
| J21. |
A. Mielke: On the justification of plate theories in linear
elasticity theory using exponential decay estimates. J. Elasticity, 38: 165-208, 1995. |
| J20. |
A. Afendikov and A. Mielke: Bifurcations of Poiseuille flow
between parallel plates: three-dimensional solutions with large spanwise
wavelength. Arch. Rational Mech. Anal., 129(2) 101-127, 1995. |
| P8. |
A. Mielke: A new approach to sideband-instabilities using the
principle of reduced instability. In A. Doelman and A. van Harten, editors,
Nonlinear dynamics and pattern formation in the natural enviroment
(Noordwijkerhout, 1994), pp. 206-222, Harlow, 1995. Longman. |
| P7. |
A. Mielke:
Homoclinic and heteroclinic solutions in two-phase
flow. In A. Mielke and K. Kirchgässner, editors. Proceedings of the
IUTAM/ISIMM Symposium on Structure and Dynamics of Nonlinear Waves in Fluids
(Hannover, 1994), pp. 353-362. World Sci. Publishing, 1995. |
|
P6. |
A. Afendikov and A. Mielke:
Instability of standing waves in large wavelength in problems
with O(2) symmetry. In "A. Mielke and K. Kirchgässner (eds):
Proceedings of the IUTAM/ISIMM Symposium on Structure and Dynamics
of Nonlinear Waves in Fluids (Hannover, 1994), World Sci. Publishing,
1995", pages 133-138.
|
| 1994 |
|
| J19. |
A. Mielke:
Floquet theory for, and bifurcations from spatially
periodic patterns. Tatra Mt. Math. Publ., 4: 153-158, 1994. Equadiff 8
(Bratislava, 1993). |
| J18. |
A. Mielke:
Essential manifolds for an elliptic problem in an
infinite strip. J. Differential Equations, 110: 322-355, 1994. |
| P5. |
A. Afendikov and A. Mielke: A spatial center manifold approach
to a hydrodynamical problem with O(2) symmetry. In P. Chossat, editor,
Dynamics, Bifurcation and Symmetry (Cargèse, 1993), pp. 1-10,
Dordrecht, 1994. Kluwer Acad. Publ. |
| 1992 |
|
| J17. |
A. Mielke: On nonlinear problems of mixed type: a qualitative
theory using infinite-dimensional center manifolds. J. Dynam. Differential
Equations, 4: 419-443, 1992. |
| J16. |
P. Kirrmann, G. Schneider, and A. Mielke: The validity of
modulation equations for extended systems with cubic
nonlinearities. Proc. Roy. Soc. Edinburgh Sect. A, 122: 85-91, 1992. |
| J15. |
A. Mielke: Reduction of PDEs on domains with several unbounded
directions: a first step towards modulation equations. Z. angew. Math,
Phys., 43(3) 449-470, 1992 |
| J14. |
G. Iooss and A. Mielke: Time-periodic Ginzburg-Landau equations
for one-dimensional patterns with large wave
length. Z. angew. Math. Phys., 43(1) 125-138, 1992. |
| J13. |
A. Mielke, P. Holmes, and O. O'Reilly. Cascades of homoclinic
orbits to, and chaos near, a Hamiltonian
saddle-center. J. Dynam. Differential Equations, 4(1) 95-126, 1992. |
|
1991
| |
|---|
| B1. |
A. Mielke: Hamiltonian and Lagrangian flows on center manifolds
with applications to elliptic variational problems. Lecture Notes in
Mathematics Vol. 1489, Springer-Verlag 1991 (vii + 140 pages). |
|
| J12. |
A. Mielke: Locally invariant manifolds for quasilinear parabolic
equations. Rocky Mountain J. Math., 21: 707-714, 1991. Current directions
in nonlinear partial differential equations (Provo, UT, 1987). |
| J11. |
G. Iooss and A. Mielke: Bifurcating time-periodic solutions of
Navier-Stokes equations in infinite cylinders. J. Nonlinear Sci., 1(1) 107-146, 1991. |
| P4. |
G. Iooss and A. Mielke: Hydrodynamical stability problems in
infinitely long cylindrical domains: existence of defects in travelling
waves. In S. Rionero, editor, Waves and stability in continuous media
(Sorrento, 1989), pp. 243-257. World Sci. Publishing, River Edge, NJ, 1991. |
|
| P3. |
G. Iooss and A. Mielke: Reduction and normalization of
hydrodynamical stability problems in infinitely long cylinders. In W. Schneider,
H. Troger, and F. Ziegler, editors, Trends in Applications of Mathematics to
Mechanics (Hollabrunn, 1989) STAMM VIII, pp. 43-56. Longman Sci. Tech.,
Harlow, 1991. |
|
1990
| |
|---|
|
J10. |
A. Mielke: Topological methods for discrete
dynamical systems. Mitt. Ges. Angew. Math. Mech.,
90/2: 19-37, 1990.
|
| J9. |
A. Mielke: Normal hyperbolicity of center manifolds and
Saint-Vernant's principle. Arch. Rational Mech. Anal., 110: 353-372, 1990. |
|
P2. |
G. Iooss, A. Mielke, and Y. Demay.
Mathematical justification of steady Ginzburg-Landau equation
starting from Navier-Stokes. In "New trends in nonlinear dynamics
and pattern-forming phenomena (Cargèse, 1988),
Plenum, New York, 1990", pages 275-286.
|
|
M2. |
A. Mielke: Hamiltonische und Lagrangesche Flüsse auf
Zentrumsmannigfaltigkeiten mit Anwendungen auf elliptische
Variationsprobleme. Habilitation thesis: Fakultät Mathematik,
Universität Stuttgart, 1990. |
|
1989
| |
|---|
|
J8. |
G. Iooss, A. Mielke, and Y. Demay.
Theory of steady Ginzburg-Landau equation in hydrodynamic stability problems.
European J. Mech. B Fluids, 8(3) 229-268, 1989.
|
|
1988
| |
|---|
|
J7. |
A. Mielke: Saint-Vernant's problem and semi-inverse
solutions in nonlinear elasticity.
Arch. Rational Mech. Anal. 102, 205-229, 1988.
(Corrigendum in 110, 351-352, 1990.)
|
| J6. |
A. Mielke: On Saint-Vernant's problem for an elastic
strip. Proc. Roy. Soc. Edinburgh Sect. A, 110: 161-181, 1988. |
| J5. |
A. Mielke and P.J. Holmes. Spatially complex equilibria of
buckled rods. Arch. Rational Mech. Anal., 101: 319-348, 1988. |
| J4. |
A. Mielke: Reduction of quasilinear elliptic equations in
cylindrical domains with applications. Math. Methods Appl. Sci., 10:
51-66, 1988. |
| P1. |
A. Mielke: On Saint-Vernant's problem and Saint-Vernant's
principle in nonlinear elasticity. In J. Besseling and W. Eckhaus, editors,
Trends in Applications of Mathematics to Mechanics (Wassenaar, 1987), STAMM
VII, pp. 252-260. Springer, Berlin, 1988. |
| 1987 |
|
| J3. |
A. Mielke: Über maximale Lp-Regularität für
Differentialgleichungen in Banach- und Hilbert-Räumen. Math. Ann.,
277: 121-133, 1987. |
|
1986
| |
|---|
|
J2. |
A. Mielke: Steady flows of inviscid fluids under localized
perturbations. J. Diff. Equations, 65: 89-116, 1986.
|
|
J1. |
A. Mielke:
A reduction principle for nonautonomous systems in
infinite-dimensional spaces.
J. Diff. Equations, 65: 68-88, 1986.
|
|
1984
| |
|---|
|
M1. |
A. Mielke:
Stationäre Lösungen der Euler-Gleichung in Kanälen
variabler Tiefe. Dissertation Thesis: Fakultät Mathematik,
Universität Stuttgart, July 1984
|
