Long time existence for the wave equation with a noise term

• 成果类型: Article
• 署名作者: Mueller, C
• 署名单位: University of Rochester
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1997
• 页码: 133-151
• 关键词: reaction-diffusion equation; non-gaussian perturbations; large deviations

摘要

We consider the equation u(tt) = Delta u + a(u)N for x is an element of R-1 or R-2. N is a Gaussian noise term, which is white noise if x is an element of R-1. If a(u) grows no faster than u(log u)(1/2-epsilon), then there is a unique solution valid for all time.