Stochastic wave equations with polynomial nonlinearity
成果类型：
Article
署名作者：
Chow, PL
署名单位：
Wayne State University
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2002
页码：
361-381
关键词：
摘要：
This paper is concerned with a class of nonlinear stochastic wave equations in R-d with d less than or equal to 3, for which the nonlinear terms are polynomial of degree m. As an example of the nonexistence of a global solution in general, it is shown that there exists an explosive solution of some cubically nonlinear wave equation with a noise term. Then the existence and uniqueness theorems for local and global solutions in Sobolev space H-1 are proven with the degree of polynomial m less than or equal to 3 for d = 3, and m greater than or equal to 2 for d = 1 or 2.