Instantaneous everywhere-blowup of parabolic SPDEs

• 成果类型: Article
• 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
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01263-7
• 发表日期: 2024
• 页码: 601-624
• 关键词: global-solutions; EXISTENCE; EQUATIONS; Finite

摘要

We consider the following stochastic heat equation partial derivative(t)u(t,x)=1/2 partial derivative(2)(x)u(t,x)+b(u(t,x))+sigma(u(t,x)) W(t,x), defined for (t,x)is an element of(0,infinity)xR, where Wdenotes space-time white noise. The function sigma is assumed to be positive, bounded, globally Lipschitz, and bounded uniformly awayfrom the origin, and the function b is assumed to be positive, locally Lipschitz and non decreasing. We prove that the Os good condition integral infinity 1dyb(y)0 and x is an element of R}=1.The main ingredients of the proof involve a hitting-time bound for a class ofdifferential inequalities (Remark 3.3), and the study of the spatial growth of stochastic convolutions using techniques from the Malliavin calculus and the Poincar & eacute; inequal-ties that were developed in Chen et al.