用乘法噪声对反应扩散方程进行正则化

arXiv - MATH - Probability Pub Date : 2024-09-17 DOI:arxiv-2409.11130

Konstantinos Dareiotis, Teodor Holland, Khoa Lê

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摘要

我们考虑由乘法时空白噪声驱动的 1+1$ 维随机反应-扩散方程，该方程的分布漂移属于任意正则指数大于 $-1$ 的 Besov-H "老空间。通过使用随机缝纫技术和马利亚文微积分相结合的方法，我们证明该方程有一个唯一的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.

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