Семинар Добрушинской математической лаборатории ИППИ РАН
16 января, вторник, 16:00, ауд. 307 (Zoom).
ссылка на Zoom: https://umd.zoom.us/j/5903871180
Леонид Коралов (Uni Maryland): Parabolic equations and diffusion
processes with degeneration: boundary problems, metastability, and
homogenization
Abstract:
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.
| 10.01.2024 | Комеч Сергей Александрович |