A SMOLUCHOWSKI-KRAMERS APPROXIMATION FOR AN INFINITE DIMENSIONAL SYSTEM WITH STATE-DEPENDENT DAMPING

• 成果类型: Article
• 署名作者: Cerrai, Sandra; Xi, Guangyu
• 署名单位: University System of Maryland; University of Maryland College Park
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/21-AOP1549
• 发表日期: 2022
• 页码: 874-904
• 关键词: small-mass limit; langevin equation; charged-particle; large deviations; brownian-motion; magnetic-field; asymptotics; EXISTENCE

摘要

We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of 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.