Parabolic equations and diffusion processes with degeneration: boundary problems, metastability, and homogenization

Stated in probabilistic terms, we describe the metastable behavior for randomly perturbed processes with invariant points or surfaces. Stated in PDE terms, the problems concern the asymptotic behavior of solutions to parabolic equations whose coefficients degenerate at the boundary of a domain. The operator may be regularized by adding a small diffusion term. Metastability effects arise in this case: the asymptotics of solutions, as the size of the perturbation tends to zero, depends on the time scale. Initial-boundary value problems with both the Dirichlet and the Neumann boundary conditions are considered. We also consider periodic homogenization for operators with degeneration. The talk is based on joint work with M. Freidlin.
ссылка на Zoom: https://umd.zoom.us/j/5903871180