Averaging principle for a class of stochastic reaction-diffusion equations

• 成果类型: Article
• 署名作者: Cerrai, Sandra; Freidlin, Mark
• 署名单位: University of Florence; University System of Maryland; University of Maryland College Park
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0144-z
• 发表日期: 2009
• 页码: 137-177
• 关键词: behavior; systems

摘要

We consider the averaging principle for stochastic reaction-diffusion equations. Under some assumptions providing existence of a unique invariant measure of the fast motion with the frozen slow component, we calculate limiting slow motion. The study of solvability of Kolmogorov equations in Hilbert spaces and the analysis of regularity properties of solutions, allow to generalize the classical approach to finite-dimensional problems of this type in the case of SPDE's.