{"title":"用乘法噪声对反应扩散方程进行正则化","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":"{\"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}","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}
Regularisation by multiplicative noise for reaction-diffusion equations
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.