A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping

Sandra Cerrai; Guangyu Xi

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arXiv · 2011.14236

A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping

Sandra Cerrai·Guangyu Xi

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Abstract

We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of $\mathbb{R}^n$ subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass limit the solution converges to the solution of a stochastic quasilinear parabolic equation where a noise-induced extra drift is created.

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Sandra Cerrai, Guangyu Xi. 2020-11-28. A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping. https://arxiv.org/abs/2011.14236

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