A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping
Analysis of PDEs
2021-10-12 v2 Probability
Abstract
We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of 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.
Cite
@article{arxiv.2011.14236,
title = {A Smoluchowski-Kramers approximation for an infinite dimensional system with state-dependent damping},
author = {Sandra Cerrai and Guangyu Xi},
journal= {arXiv preprint arXiv:2011.14236},
year = {2021}
}