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A. Jüngel:
"Stochastic PDEs, Coercive inequalities and numerical modeling";
Talk: CNRS-PAN Mathematics Summer Institute, Krakau; 2015-06-28 - 2015-07-04.

Entropy-dissipation methods have been developed recently to investigate the qualitative behavior of solutions to nonlinear partial differential equations and to derive explicit or optimal constants in convex Sobolev inequalities. It turned out that these methods also help for the global existence analysis and the design of stable numerical schemes. In this lecture series, we will highlight some of the aspects of entropy methods, in particular for linear and nonlinear Fokker-Planck equations, cross-diffusion systems from biology, and Maxwell-Stefan systems for multicomponent fluid mixtures. New analytical tools are the boundedness-by-entropy principle and systematic integration by parts. Connections to Markov processes will be highlighted too.