Artur Stephan's homepage


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Welcome to the home page of Artur Stephan.

I am a researcher in the group Partial Differential Equations at WIAS.

My contact details are here.







Scientific interests

  • Variational methods for evolution equations, ordinary and partial differential equations. Convex analysis and (Evolutionary) Gamma-convergence.
  • Applications to classical and quantum mechanics; reaction and reaction-diffusion systems.
  • Multi-scale problems and mathematical coarse-graining.
  • Operator theory and semigroup theory; Markov processes; split-step approximations with convergence rate estimates.
  • Numerical analysis




Publications



You find preprints of my published papers also on arXiv. Otherwise, please contact me.



Submitted publications:

  • A. Mielke, R. Rossi, A. Stephan: "On time-splitting methods for gradient flows with two dissipation mechanisms", preprint on arXiv, July 2023.
  • A. Stephan: "Trotter-type formula for operator semigroups on product spaces", preprint on arXiv, July 2023.
  • A. Stephan, H. Stephan: "Positivity and polynomial decay of energies for square-field operators", preprint on arXiv, December 2021.
  • A. Stephan: "Coarse-graining and reconstruction for Markov matrices", preprint on arXiv, October 2021.

    Published articles:

  • M. Heida, M. Kantner, A. Stephan: "Consistency and convergence for a family of finite volume discretizations of the Fokker--Planck operator", ESAIM:M2AN 55.6 (2021), 25 pages, DOI:10.1051/m2an/2021078.
  • A. Stephan: "EDP-convergence for a linear reaction-diffusion system with fast reversible reaction", Calc. Var. PDE 60.226 (2021), 35 pages, DOI:10.1007/s00526-021-02089-0.
  • A. Mielke, M. A. Peletier, A. Stephan: "EDP-convergence for nonlinear fast-slow reaction systems with detailed balance", Nonlinearity 34.8 (2021), pp. 5762-5798, DOI:10.1088/1361-6544/ac0a8a.
  • A. Mielke, A. Stephan: "Coarse-graining via EDP-convergence for linear fast-slow reaction systems", Math. Mod. Meth. Appl. Sci. 30.09 (2020), pp. 1765-1807, DOI:10.1142/S0218202520500360.
  • H. Neidhardt, A. Stephan, V. A. Zagrebnov: "Convergence Rate Estimates for Trotter Product Approximations of Solution Operators for Non-autonomous Cauchy Problems", Pub. Res. I. Math. Sci. 56.1 (2020), pp. 83-135, DOI:10.4171/PRIMS/56-1-5.
  • A. Stephan, H. Stephan: "Memory equations as reduced Markov processes", Discr. Cont. Dyn. Systems 39.4 (2019), pp.2133-2155, DOI:10.3934/dcds.2019089.
  • H. Neidhardt, A. Stephan, V. A. Zagrebnov: "Trotter Product Formula and Linear Evolution Equations on Hilbert Spaces", Analysis and Operator Theory. Springer Optimization and Its Applications, vol. 146 (2019), pp. 271-299, DOI:10.1007/978-3-030-12661-2_13.
  • H. Neidhardt, A. Stephan, V. A. Zagrebnov: "Remarks on the operator-norm convergence of the Trotter product formula", Int. Equ. Op. Th. 90.15 (2018), 14 pages, DOI:10.1007/s00020-018-2424-z.
  • H. Neidhardt, A. Stephan, V. A. Zagrebnov: "Operator-Norm Convergence of the Trotter Product Formula on Hilbert and Banach Spaces: A Short Survey", Current Research in Nonlinear Analysis. Springer Optimization and Its Applications, vol.135 (2018), pp. 229-247, DOI:10.1007/978-3-319-89800-1_9.
  • V. Klinshov, S. Yanchuk, A. Stephan, V. Nekorkin: "Phase response function for oscillators with strong forcing or coupling", EPL (Europhysics Letters) 118.5 (2017), DOI:10.1209/0295-5075/118/50006.
  • H. Neidhardt, A. Stephan, V. A. Zagrebnov: "On convergence rate estimates for approximations of solution operators for linear non-autonomous evolution equations", Nanosystems: physics, chemistry, mathematics 8.2 (2017), pp. 202-215, DOI:10.17586/2220-8054-2017-8-2-202-215.

    Proceedings and miscellaneous:

  • A. Stephan: "EDP-convergence for nonlinear fast-slow reaction systems", Oberwolfach Report 2038: Variational Methods for Evolution (2020), DOI:10.14760/OWR-2020-29.
  • A. Stephan: "On EDP-convergence for gradient systems with different time scales", Proc. Appl. Math. Mech. (PAMM) (2019), DOI:10.1002/pamm.201900366.
  • A. Stephan: "Combinatorial considerations on the invariant measure of a stochastic matrix", preprint on arXiv, (2019).

    Theses:

  • A. Stephan: Coarse-graining for gradient systems and Markov processes, Dissertation, Humboldt-Universität zu Berlin, (2021), xii + 210 pages, DOI:10.18452/23529.
  • A. Stephan: On operator-norm estimates for approximations of solutions of evolution equations using the Trotter product formula, Master thesis, Humboldt-Universität zu Berlin, (2016), 69 pages, link.




    • Miscellaneous

    • Media
      I gave a talk at the 6th BMS Student Conference on the Hamilton-Jacobi equation. The talk has been recorded.
    • Membership
      I am a member of the GAMM Activity Group "Analysis of Partial Differential Equations".
    • PhD-student representative
      I was the PhD-student representative in WIAS Berlin from 2018 to 2020.
    • I am also on ResearchGate.

    © Artur Stephan. Last modified: January 2023.