{"title":"On a reaction diffusion problem with a moving impulse on boundary","authors":"Alioune Coulibaly","doi":"10.1515/rose-2023-2023","DOIUrl":null,"url":null,"abstract":"Abstract We study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"10 19","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/rose-2023-2023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract We study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.