STOCHASTIC HEAT EQUATION WITH ROUGH DEPENDENCE IN SPACE

• 成果类型: Article
• 署名作者: Hu, Yaozhong; Huang, Jingyu; Le, Khoa; Nualart, David; Tindel, Samy
• 署名单位: University of Kansas; Purdue University System; Purdue University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1172
• 发表日期: 2017
• 页码: 4561-4616
• 关键词: Existence

摘要

This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter H is an element of (1/4, 1/2) in the space variable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient sigma(u) is differentiable with a Lipschitz derivative and sigma(0) = 0.