Analysis Seminar
主講者: 1.Ansgar Jungel (Vienna University of Technology) 2.林俊良博士(中研院數學所)
講題: 1.Entropy-dissipation methods for nonlinear partial differential equations 2.Invariant manifords for steady Boltzmann equation(10)
時間: 2012-11-19 (Mon.)  10:00 - 13:00
地點: 數學所 617 研討室 (台大院區)
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.
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