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Wednesday, 01.03.2017, 15.15 Uhr (WIAS-406)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. P. Colli, University of Pavia, Italien:
About a non-smooth regularization of a forward-backward parabolic equation
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
A variation of the Cahn-Hilliard equation, describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation is discussed. In the concerned system, the general viscous regularization is expressed by a maximal monotone graph acting on the time derivative of the concentration and presenting a strong coerciveness property. The phase variable stands for the concentration of a chemical species and it evolves under the influence of a non-convex free energy density. For the chemical potential a non-homogeneous Dirichlet boundary condition is assumed. Existence and continuous dependence results are shown. The talk reports on a joint work with E. Bonetti and G. Tomassetti.

Further Informations
Berliner Oberseminar ``Nichtlineare Partielle Differentialgleichungen'' (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Thursday, 02.03.2017, 09.00 Uhr (WIAS-406)
Halbleiterseminar
Dr. D. H. Doan, WIAS:
A unified Scharfetter Gummel scheme
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Further Informations
Halbleiterseminar

Host
WIAS Berlin
Thursday, 02.03.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. L. O. Müller, Norwegian University of Science and Technology:
A local time stepping solver for one-dimensional blood flow
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We present a finite volume solver for one-dimensional blood flow simulations in networks of elastic and viscoelastic vessels, featuring high-order space-time accuracy and local time stepping (LTS). The solver is built on:
(i) a high-order finite-volume type numerical scheme,
(ii) a high-order treatment of the numerical solution at internal vertexes of the network (junctions);
(iii) an accurate LTS strategy.
Several applications of the method will be presented. First, we apply the LTS scheme to the Anatomically Detailed Arterial Network model (ADAN), comprising 2142 arterial vessels. Second, we show results of a computational study where the ADAN model is coupled to automatically generated microvascular networks in order to elucidate aspects on the pathopysiology of small vessel disease for cerebral arteries.

Host
WIAS Berlin
Friday, 03.03.2017, 10.00 Uhr (WIAS-ESH)
Seminar Partielle Differentialgleichungen
S. Melchionna, University of Vienna, Österreich:
A variational approach to symmetry, monotonicity and comparison for doubly-nonlinear equations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including gradient flows, some nonlocal problems, and systems of nonlinear parabolic equations. Our method is based on the so-called Weighted-Energy-Dissipation (WED) variational approach. This consists in defining a global parameter-dependent functional over entire trajectories and proving that its minimizers converge to solutions to the target problem as the parameter goes to zero. Qualitative properties and comparison principles can be easily proved for minimizers of the WED functional and, by passing to the limit, for the limiting problem. Several applications of the abstract results to systems of nonlinear PDEs and to fractional/nonlocal problems are presented.

Further Informations
Seminar Partielle Differentialgleichungen

Host
WIAS Berlin