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- W2808285626 abstract "We prove 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, both with Lipschitz-continuous and with polynomial non-linearities. In particular, we prove that 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. The Wasserstein metric is associated to a suitable distance on the space of square integrable functions, that is chosen in such a way that the dynamics of the limiting stochastic parabolic equation is contractive with respect to such a Wasserstein metric. This implies that the limiting result is a consequence of the validity of a generalized Smoluchowski-Kramers limit at fixed times. The proof of such a generalized limit requires new delicate bounds for the solutions of the stochastic wave equation, that must be uniform with respect to the size of the mass." @default.
- W2808285626 created "2018-06-21" @default.
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- W2808285626 date "2018-06-14" @default.
- W2808285626 modified "2023-09-27" @default.
- W2808285626 title "On the convergence of stationary solutions in the Smoluchowski-Kramers approximation of infinite dimensional systems" @default.
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