{"title":"Generalized Stochastic Burgers' Equation with Non-Lipschitz Diffusion Coefficient","authors":"Vivek Kumar, Ankik Kumar Giri","doi":"10.31390/COSA.12.3.06","DOIUrl":null,"url":null,"abstract":"In this article, we study the existence of weak solutions to the one-dimensional generalized stochastic Burgers’ equation with polynomial nonlinearity perturbed by space-time white noise with Dirichlet boundary conditions and α-Hölder continuous coefficient in noise term, where α ∈ [1/2, 1). The existence of weak solutions is shown by solving an equivalent martingale problem.","PeriodicalId":53434,"journal":{"name":"Communications on Stochastic Analysis","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications on Stochastic Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31390/COSA.12.3.06","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 2
Abstract
In this article, we study the existence of weak solutions to the one-dimensional generalized stochastic Burgers’ equation with polynomial nonlinearity perturbed by space-time white noise with Dirichlet boundary conditions and α-Hölder continuous coefficient in noise term, where α ∈ [1/2, 1). The existence of weak solutions is shown by solving an equivalent martingale problem.
期刊介绍：
The journal Communications on Stochastic Analysis (COSA) is published in four issues annually (March, June, September, December). It aims to present original research papers of high quality in stochastic analysis (both theory and applications) and emphasizes the global development of the scientific community. The journal welcomes articles of interdisciplinary nature. Expository articles of current interest will occasionally be published. COSAis indexed in Mathematical Reviews (MathSciNet), Zentralblatt für Mathematik, and SCOPUS
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