Large-time behaviour of solutions to certain evolutionary problems.

Abstract:  This talk aims to demonstrate certain techniques used in arriving at convergence (to equilibrium states) results for solutions to certain time-evolution problems in statistical physics. One of the methods that we emphasize is the entropy method which avoids linearisation and(or) compactness arguments to yield decay estimates with constants and rates, which can be calculated (in principle) explicitly. We will try to appreciate these methods via examples: the heat equation, the Fokker-Planck equation, the linear Boltzmann equation, the Bhatnagar-Gross-Krook equation et cetera. If time permits, we shall also address the effect of degeneracy in these equations on the decay estimates. This talk will be elementary and accessible to anyone with basic PDE knowledge.