Work

On the local well-posedness of randomly forced reaction-diffusion equations with $$\varvec{L^2}$$ initial data and a superlinear reaction term

Year: 2026

Type: article

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 $$L\log L$$ L log L growth condition. We prove that the SPDE is well posed when the initial data is in $$L^2[0,1]$$ L 2 [ 0 , 1 ] . This solves a strong form of an open problem.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-026-01487-9

Authors: Mohammud Foondun, Davar Khoshnevisan, Eulalia Nualart

Institutions: University of Strathclyde, University of Utah, Universitat Pompeu Fabra, Barcelona School of Economics

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Leverhulme Trust