{"title":"Regularisation by multiplicative noise for reaction-diffusion equations","authors":"Konstantinos Dareiotis, Teodor Holland, Khoa Lê","doi":"arxiv-2409.11130","DOIUrl":null,"url":null,"abstract":"We consider the stochastic reaction-diffusion equation in $1+1$ dimensions\ndriven by multiplicative space-time white noise, with a distributional drift\nbelonging to a Besov-H\\\"older space with any regularity index larger than $-1$.\nWe assume that the diffusion coefficient is a regular function which is bounded\naway from zero. By using a combination of stochastic sewing techniques and\nMalliavin calculus, we show that the equation admits a unique solution.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","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-2409.11130","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 consider the stochastic reaction-diffusion equation in $1+1$ dimensions
driven by multiplicative space-time white noise, with a distributional drift
belonging to a Besov-H\"older space with any regularity index larger than $-1$.
We assume that the diffusion coefficient is a regular function which is bounded
away from zero. By using a combination of stochastic sewing techniques and
Malliavin calculus, we show that the equation admits a unique solution.