On the stochastic Burgers' equation in the real line

• 成果类型: Article
• 署名作者: Gyöngy, I; Nualart, D
• 署名单位: University of Edinburgh; University of Barcelona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1999
• 页码: 782-802
• 关键词: partial-differential equations

摘要

In this paper we establish the existence and uniqueness of an L-2(R)-valued solution for a one-dimensional Burgers' equation perturbed by a space-time white noise on the real Line. We show that the solution is continuous in space and time, provided the initial condition is continuous. The main ingredients of the proof are maximal inequalities for the stochastic convolution, and some a priori estimates far a class of deterministic parabolic equations.