Local large deviations for randomly forced nonlinear wave equations with localized damping

2024/09/18 by Chen, Yuxuan, Liu, Ziyu, Xiang, Shengquan +1 · 2 citations
#35L71 #37L50 #60B12 #60F10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2409.11717

Abstract

We study the large deviation principle (LDP) for locally damped nonlinear wave equations perturbed by a bounded noise. When the noise is sufficiently non-degenerate, we establish the LDP for empirical distributions with lower bound of a local type. The primary challenge is the lack of compactness due to the absence of smoothing effect. This is overcome by exploiting the asymptotic compactness for the dynamics of waves, introducing the concept of asymptotic exponential tightness for random measures, and establishing a new LDP approach for random dynamical systems.

Cited by

• Donsker-Varadhan large deviation principle for locally damped and randomly forced NLS equations
• Exponential mixing for Korteweg-de Vries equation with localized noise

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