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Regularisation by multiplicative noise for reaction-diffusion equations

delete2026-03-01
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PRE
AI
D
Dareiotis, Konstantinos
H
Holland, Teodor
L
Le, Khoa *
DOI：10.1007/s00440-026-01474-0delete
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Abstract

Abstract

En 中文
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.
Keywords:
TIME WHITE-NOISE
DIFFERENTIAL-EQUATIONS
LATTICE APPROXIMATIONS
DRIVEN
CONVERGENCE
SPDES
ROUGH

Journal

P
Probability Theory and Related Fields
IF:
1.6
Papers:
61
Citations:
0

Organization

U
university of leeds
Scholars:
3.5W
Papers: 3.3W
Citations: 45
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