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Universität Augsburg
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Universität Augsburg
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Dr. Nicola Zamponi
Universität Augsburg
spricht am
Mittwoch, 15. April 2026
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| Physical systems including many components (or species) whose time evolution is mainly driven by diffusion appear in many problems coming from the applied sciences. These systems are often described by a set of (nonlinear) evolutionary partial differential equations (PDEs) for concentrations or densities featuring so-called cross diffusion, a strong coupling between the equations where the diffusion of a species is influenced by the density gradient of other species. Some interesting mathematical questions concerning these PDEs systems are the (global in time) existence of (weak) solutions, as well as (weak-strong) uniqueness, long-time behavior, boundedness and regularity in Hölder or Sobolev spaces of such solutions. Answering these questions is often challenging since the presence of cross-diffusion prevents the application of many standard analytical methods (e.g. straightforward monotonicity/coercivity arguments, maximum principles). We present some techniques for the analysis of these systems based on the concept of mathematical entropy and we apply them to some specific equations, such as: a model for rival gangs interaction in a city; an incompressible fluid model of electrically charged, chemically reacting and heat conducting mixtures; a class of population models. |
| Hierzu ergeht herzliche Einladung. |
| Prof. Dr. Jan-Frederik Pietschmann |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).