On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction

TL;DR

This paper investigates the behavior of stochastic nonlinear damped wave equations with state-dependent friction in the combined small mass and noise limit, establishing a large deviation principle for this regime.

Contribution

It provides the first analysis of large deviations for nonlinear wave equations with variable friction in the small noise and mass limit.

Findings

Established a large deviation principle in the joint small mass and noise limit.

Extended the analysis to Klein-Gordon type stochastic wave equations with state-dependent friction.

Provided insights into the asymptotic behavior of solutions under combined small parameters.

Abstract

We study the validity of a large deviation principle for a class of stochastic nonlinear damped wave equations, of Klein-Gordon type, in the joint small mass and small noise limit. The friction term is assumed to be state dependent.