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Summary: Lecture notes for XXVII Summer school in
mathematical physics Ravello, Italy, September 9-21,
2002
Entropy method and the large-time
behavior of parabolic equations
Anton Arnold
Institut für Numerische und Angewandte Mathematik
Universität Münster
Einsteinstr. 62
D-48149 Münster, Germany.
22nd October 2009
http://www.anum.tuwien.ac.at/arnold/ Email: anton.arnold@tuwien.ac.at
Contents
1 Large-time behavior of heat and linear Fokker-Planck equations 5
2 Entropy method for symmetric diffusion equations & non-symmetric exten-
sions 9
3 Logarithmic & convex Sobolev inequalities 15
4 Pertubation results & application to semi-linear models 21
5 Entropy method for quasi-linear equations 25
6 Diffusion equations as gradient flows 29
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