Nonlinear stochastic perturbations of dynamical systems and quasi-linear parabolic PDE's with a small parameter

• 成果类型: Article
• 署名作者: Freidlin, M.; Koralov, L.
• 署名单位: 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/s00440-009-0208-8
• 发表日期: 2010
• 页码: 273-301
• 关键词: metastability; approximation; resonance

摘要

In this paper, we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion processes. In particular, we discuss the exit problem and metastability for the processes corresponding to quasi-linear initial-boundary value problems.