Conservative stochastic cahn-hillrard equation with reflection

• 成果类型: Article
• 署名作者: Debussche, Arnaud; Zambotti, Lorenzo
• 署名单位: Universite Paris Cite; Sorbonne Universite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000773
• 发表日期: 2007
• 页码: 1706-1739
• 关键词: phi interface model; hilliard equation; parts formulas; spdes; fluctuations; integration; noise; wall

摘要

We consider a stochastic partial differential equation with reflection at 0 and with the constraint of conservation of the space average. The equation is driven by the derivative in space of a space-time white noise and contains a double Laplacian in the drift. Due to the lack of the maximum principle for the double Laplacian, the standard techniques based on the penalization method do not yield existence of a solution. We propose a method based on infinite dimensional integration by parts formulae, obtaining existence and uniqueness of a strong solution for all continuous nonnegative initial conditions and detailed information on the associated invariant measure and Dirichlet form.