On a nonlinear stochastic wave equation in the plane: Existence and uniqueness of the solution

• 成果类型: Article
• 署名作者: Millet, A; Morien, PL
• 署名单位: Sorbonne Universite; Sorbonne Universite; Universite Paris Cite; Universite Paris Nanterre
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2001
• 页码: 922-951
• 关键词: dimensions; noise

摘要

In this paper, we investigate the existence and uniqueness of the solution for a class of stochastic wave equations in two space-dimensions containing a non-linearity of polynomial type. The method used in the proofs combines functional analysis arguments with probabilistic tools, and further estimates for the Green function associated with the classical wave equation.