Math Colloquium: Large-Time Asymptotics in the Smoluchowski-Kramers Approximation of Infinite...
Wednesday, February 6, 2019
3:00 PM-4:00 PM
Title: Large-Time Asymptotics in the Smoluchowski-Kramers Approximation of Infinite Dimensional Systems
Sandra Cerrai, University of Maryland
Abstract: I will discuss the validity of the so-called Smoluchowski-Kramers approximation for systems with an infinite number of degrees of freedom in a finite time. Then, I will investigate the validity of such approximation for large time. In particular, I will address the problem of the convergence, in the small mass limit, of statistically invariant states for a class of semi-linear damped wave equations, perturbed by an additive Gaussian noise, with quite general nonlinearities. More precisely, I will show how the first marginals of any sequence of invariant measures for the stochastic wave equation converge in a suitable Wasserstein metric to the unique invariant measure of the limiting stochastic semi-linear parabolic equation obtained in the Smoluchowski-Kramers approximation.
Korman Center, Room 245, 15 S 33rd Street, Philadelphia PA, 19104