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

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arxiv 2409.11717 v1 pith:WIE6F2OP submitted 2024-09-18 math.AP math.OCmath.PR

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

Yuxuan Chen , Ziyu Liu , Shengquan Xiang , Zhifei Zhang This is my paper
classification math.AP math.OCmath.PR
keywords asymptoticcompactnessequationslargelocalnoisenonlinearrandom
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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.

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Cited by 3 Pith papers

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  1. Exponential mixing for Korteweg-de Vries equation with localized noise

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    Weakly damped KdV on a circle with bounded localized random forcing is exponentially mixing: a unique invariant measure exists and attracts all initial data in L2.

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    The 1D stochastic Allen-Cahn equation with localized white noise admits a unique invariant measure and its Markov process is exponentially mixing.

  3. Exponential mixing for nonlinear Schr\"odinger equations perturbed by bounded degenerate noise

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