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A. Jüngel:
"Entropy-dissipation methods for nonlinear partial differential equations";
Keynote Lecture: Analysis Seminar, Institute of Mathematics, Academia Sinica of Taiwan, Taipei, Taiwan (invited); 2012-11-19.

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. In this talk, we explain some aspects of these methods
related to higher-order parabolic equations and cross-diffusion systems.
The mathematical tools are systematic integration by parts and entropy
variable formulations. The first tool is related to decision problems
in real algebraic geometry, whereas the second tool has connections
to non-equilibrium thermodynamics. The considered differential equations
have applications in quantum semiconductor theory and cell biology.

Siehe englisches Abstract.

Entropy variables; polynomial decision problem; nonlinear PDEs