On the local well-posedness of randomly forced reaction-diffusion equations with $L^2$ initial data and a superlinear reaction term
Probability
2026-03-26 v2
Abstract
We consider a parabolic stochastic partial differential equation (SPDE) on that is forced with multiplicative space-time white noise with a bounded and Lipschitz diffusion coefficient and a drift coefficient that is locally Lipschitz and satisfies an growth condition. We prove that the SPDE is well posed when the initial data is in . This solves a strong form of an open problem.
Keywords
Cite
@article{arxiv.2510.00214,
title = {On the local well-posedness of randomly forced reaction-diffusion equations with $L^2$ initial data and a superlinear reaction term},
author = {Mohammud Foondun and Davar Khoshnevisan and Eulalia Nualart},
journal= {arXiv preprint arXiv:2510.00214},
year = {2026}
}