Perturbations of Parabolic Equations and Diffusion Processes with Degeneration: Boundary Problems and Metastability

Abstract: We study diffusion processes in a bounded domain with absorbing or reflecting boundary. The generator of the process is assumed to contain two terms: the main term that degenerates on the boundary in a direction orthogonal to the boundary and a small non-degenerate perturbation. Understanding the behavior of such processes allows us to study the stabilization of solutions to the corresponding parabolic equations with a small parameter. 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 Dirichet and the Neumann boundary conditions will be considered. The talk is based on joint work with M. Freidlin.

mathematical physicsprobability

Audience: researchers in the topic

Probability and the City Seminar

Series comments: The Probability and the City Seminar is organized jointly by the probability groups of Columbia University and New York University.

Video recordings of talks are posted online at www.youtube.com/channel/UC0CXjG-ZSIZHy0S40Px2FEQ .