Stabilization by noise for a class of stochastic reaction-diffusion equations

• 成果类型: Article
• 署名作者: Cerrai, S
• 署名单位: University of Florence; Scuola Normale Superiore di Pisa
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-004-0421-4
• 发表日期: 2005
• 页码: 190-214
• 关键词: partial-differential-equations; invariant-measures; large deviations; systems; exponent

摘要

We prove uniqueness, ergodicity and strongly mixing property of the invariant measure for a class of stochastic reaction-diffusion equations with multiplicative noise, in which the diffusion term in front of the noise may vanish and the deterministic part of the equation is not necessary asymptotically stable. To this purpose, we show that the L-1-norm of the difference of two solutions starting from any two different initial data converges P-a.s. to zero, as time goes to infinity.