On the local well-posedness of randomly forced reaction-diffusion equations with L2 initial data and a superlinear reaction term

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Foondun, Mohammud and Khoshnevisan, Davar and Nualart, Eulalia (2025) On the local well-posedness of randomly forced reaction-diffusion equations with L2 initial data and a superlinear reaction term. Other. arXiv, Ithaca, NY. (https://doi.org/10.48550/arXiv.2510.00214)

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Abstract

We consider a parabolic stochastic partial differential equation (SPDE) on [0,1] 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 L log L growth condition. We prove that the SPDE is well posed when the initial data is in L2[0,1]. This solves a strong form of an open problem.

ORCID iDs

Foondun, Mohammud ORCID logoORCID: https://orcid.org/0000-0001-7634-916X, Khoshnevisan, Davar and Nualart, Eulalia;
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