DISSIPATION AND HIGH DISORDER
成果类型：
Article
署名作者：
Chen, Le; Cranston, Michael; Khoshnevisan, Davar; Kim, Kunwoo
署名单位：
Utah System of Higher Education; University of Utah; University of California System; University of California Irvine
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/15-AOP1040
发表日期：
2017
页码：
82-99
关键词：
摘要：
Given a field {B(x)}x is an element of Z(d) of independent standard Brownian motions, indexed by Z(d), the generator of a suitable Markov process on Z(d), G, and sufficiently nice function sigma : [0, infinity) (bar right arrow) [0, infinity), we consider the influence of the parameter lambda on the behavior of the system, du(t) (x) = (Gu(t))(x) dt + lambda sigma(u(t)(x)) dB(t)(x) [t > 0, x is an element of Z(d)], u(0)(x) = c(0)delta(0)(x). We show that for any lambda > 0 in dimensions one and two the total mass Sigma(x is an element of Zd) u(t) (x) converges to zero as t -> infinity while for dimensions greater than two there is a phase transition point lambda(c) is an element of (0, infinity) such that for lambda > lambda(c), Sigma(x is an element of Zd) u(t) (x) -> 0 as t -> infinity while for lambda < lambda(c), Sigma(x is an element of Zd) u(t) (x) negated right arrow 0 as t -> infinity.