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

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• Sandra Cerrai (University of Maryland, College Park; University of Maryland, College Park)
• Friday 30 November 2018, 11:00-12:30
• Seminar Room 2, Newton Institute.

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SRQ - Scaling limits, rough paths, quantum field theory

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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