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

Mohammud Foondun; Davar Khoshnevisan; Eulalia Nualart

doi:10.48550/arXiv.2510.00214

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

Mohammud Foondun
, Davar Khoshnevisan
, Eulalia Nualart

Mathematics And Statistics

Research output: Working paper/Preprint/Pre-registration › Working Paper/Preprint

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.

Original language	English
Place of Publication	Ithaca, NY
Number of pages	29
DOIs	https://doi.org/10.48550/arXiv.2510.00214
Publication status	Published - 30 Sept 2025

Funding

Research supported by the Leverhulme Trust Fellowship IF-2025-040, the US-NSF grants DMS1855439 and DMS-2245242, the Spanish MINECO grant PID2022-138268NB-100, and Ayudas Fundacion BBVA a Proyectos de Investigación Científica 2021.

Keywords

SPDEs
space-time white noise
existence and uniqueness

Access to Document

10.48550/arXiv.2510.00214Licence: Other

Foondun-etal-arXiv-2025-On-the-local-well-posedness-of-randomly-forced-reaction-diffusion-equationsFinal published version, 756 KBLicence: Strath_1

Cite this

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