{"title":"The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation","authors":"Xiuwei Yin, Guangjun Shen, Jiang-Lun Wu","doi":"10.1142/s0219530521500172","DOIUrl":null,"url":null,"abstract":"In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s0219530521500172","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.
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