Cours de Christian Schmeiser, Université de Vienne et Chaire d’excellence FSMP

Entropy Methods

An overview over recently developed methods for proving decay to equilibrium for dissipative dynamical systems is presented. The methodology is based on Lyapunov functionals, often with the physical interpretation of a (generalized) entropy or free energy. The course features a short formal introduction to stochastic processes, aimed at an audience with a PDE background. The concepts of martingales and time reversal of homogeneous Markov processes are used to derive local decay results for relative entropies. These are applied to various examples of Levy processes, including applications in kinetic transport theory, in mathematical biology, and in chemical reaction networks. Quantitative decay results are derived from entropy-entropy decay inequalities or from inequalities between entropy decay and its time derivative, i.e. by the celebrated Bakry-Emery approach. A focus is on hypocoercive problems, where decay to equilibrium holds despite the fact that the decay term for the natural entropy functionals is only semi-definite. Various recent approaches to such problems, mainly in kinetic theory, are compared and unified. Finally, examples of nonlinear problems are discussed, and the question of structural assumptions allowing for entropy decay is examined.

Dedicated website FSMP

Schedule

  • Lundi 08/10 14h-17h Salle 314: video
  • Lundi 15/10 14h-17h Salle 314: video
  • Lundi 22/10 14h-17h Salle 314: video
  • Lundi 29/10 14h-17h Salle 201: video
  • Lundi 05/11 14h-17h Salle 314: video
  • Lundi 12/11 14h-17h Salle 314: video
  • Mercredi 21/11 14h-17h Salle 314: video
  • Lundi 26/11 14h-17h Salle 314:

Lecture notes (under construction)

Institut Henri Poincaré, 11 rue Pierre et Marie Curie 75005 Paris

Remerciements à G. Octavia et à l'équipe de la FSMP pour la mise en ligne des vidéos.

  • anr-efi/events/schmeiser18.txt
  • Dernière modification: 2018/11/28 06:19
  • de Jean Dolbeault