Selected topics in transport phenomena: deterministic and probabilistic aspects

Asymptotic problems for PDE's and a motion on the simplex of invariant measures

Mark Freidlin

University of Maryland

I will consider various asymptotic problems from a common point of view. Long-time effects of deterministic and stochastic perturbations of dynamical systems and semi-flows, initial-boundary problems for second order PDE's depending on a small parameter, homogenization problems, wave fronts in Reaction-Diffusion equations will be considered. One can identify a slow and a fast components of the time evolution in these problems and describe the limiting long-time behavior as a motion on the simplex of normalized invariant measures of an appropriate non-perturbed system.