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

Abstract

We study the validity of a large deviation principle for a class of stochastic nonlinear damped wave equations, including equations of Klein-Gordon type, in the joint small mass and small noise limit. The friction term is assumed to be state dependent. We also provide the proof of the Smolchowski-Kramers approximation for the case of variable friction, non-Lipschitz nonlinear term and unbounded diffusion.