{"title":"Local large deviations for randomly forced nonlinear wave equations with localized damping","authors":"Yuxuan Chen, Ziyu Liu, Shengquan Xiang, Zhifei Zhang","doi":"arxiv-2409.11717","DOIUrl":null,"url":null,"abstract":"We study the large deviation principle (LDP) for locally damped nonlinear\nwave equations perturbed by a bounded noise. When the noise is sufficiently\nnon-degenerate, we establish the LDP for empirical distributions with lower\nbound of a local type. The primary challenge is the lack of compactness due to\nthe absence of smoothing effect. This is overcome by exploiting the asymptotic\ncompactness for the dynamics of waves, introducing the concept of asymptotic\nexponential tightness for random measures, and establishing a new LDP approach\nfor random dynamical systems.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11717","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.