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

Cerrai, Sandra; Xie, Mengzi

doi:10.1090/tran/8946

On the small noise limit in the Smoluchowski-Kramers approximation of nonlinear wave equations with variable friction
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by Sandra Cerrai and Mengzi Xie;

Trans. Amer. Math. Soc. 376 (2023), 7651-7689

DOI: https://doi.org/10.1090/tran/8946

Published electronically: August 17, 2023

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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.

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