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arXiv · 2409.11130

Regularisation by multiplicative noise for reaction-diffusion equations

Konstantinos Dareiotis·Teodor Holland·Khoa Lê
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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.

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Konstantinos Dareiotis, Teodor Holland, Khoa Lê. 2024-09-17. Regularisation by multiplicative noise for reaction-diffusion equations. https://arxiv.org/abs/2409.11130

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