Lenoid Koralov, University of Maryland

Abstract: We will discuss several asymptotic problems for randomly perturbed flows. One class of flows (with regions where a strong flow creates a trapping mechanism) leads to a new class of boundary value problems with non-standard boundary conditions. We will also discuss how large-deviation techniques can be used to study the asymptotic behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding diffusion processes.