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Large time behavior of infinite dimensional systems under the Smoluchowski-Kramers approximation

Presented by: 
Sandra Cerrai
Friday 30th November 2018 - 11:00 to 12:30
INI Seminar Room 2
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.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons