Intermittency for stochastic partial differential equations driven by strongly inhomogeneous space-time white noises

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:264

Article

Xie, Bin¹ 

[1] Shinshu Univ, Fac Sci, Dept Math Sci, 3-1-1 Asahi, Matsumoto, Nagano 3908621, Japan

关键词: Stochastic partial differential equation;    Inhomogeneous noise;    Lyapunov exponent;    Intermittency;    Noise excitation;   

DOI  :  10.1016/j.jde.2017.09.028

来源: Elsevier

【 摘 要 】

In this paper, the main topic is to investigate the intermittent property of the one-dimensional stochastic heat equation driven by an inhomogeneous Brownian sheet, which is a noise deduced from the study of the catalytic super-Brownian motion. Under some proper conditions on the catalytic measure of the inhomogeneous Brownian sheet, we show that the solution is weakly full intermittent based on the estimates of moments of the solution. In particular, it is proved that the second moment of the solution grows at the exponential rate. The novelty is that the catalytic measure relative to the inhomogeneous noise is not required to be absolutely continuous with respect to the Lebesgue measure on R. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free