Regularisation by multiplicative noise for reaction-diffusion equations

• 成果类型: Article
• 署名作者: Dareiotis, Konstantinos; Holland, Teodor; Le, Khoa
• 署名单位: University of Leeds
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01474-0
• 发表日期: 2026-08
• 页码: 1625-1697
• 关键词: TIME WHITE-NOISE; differential-equations; lattice approximations; driven; CONVERGENCE; spdes; rough

摘要

We consider the stochastic reaction-diffusion equation in 1+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1+1$$\end{document} dimensions driven by multiplicative space-time white noise, with a distributional drift belonging to a Besov-H & ouml;lder space with any regularity index strictly larger than -1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-1$$\end{document}. 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.