Speaker : | 1.Ansgar Jungel (Vienna University of Technology) 2.Dr. Chun-Liang Lin (Academia Sinica) |
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Title : | 1.Entropy-dissipation methods for nonlinear partial differential equations 2.Invariant manifords for steady Boltzmann equation(10) |
Time : | 2012-11-19 (Mon) 10:00 - 13:00 |
Place : | Seminar Room 617, Institute of Mathematics (NTU Campus) |
Abstract: | 1.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. |