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

• 成果类型: Article; Early Access
• 署名作者: Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulalia
• 署名单位: University of Strathclyde; Utah System of Higher Education; University of Utah; Pompeu Fabra University; Barcelona School of Economics
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01487-9
• 发表日期: 2026-04-13
• 关键词: SPDEs; Space-time white noise; Existence and uniqueness; LONG-TIME EXISTENCE; heat-equation; multiplicative noise; global-solutions; REGULARITY; Finite

摘要

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