NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY

论文摘要

In this article, we study the nonlinear stochastic heat equation in the spatial domain Rd subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang’s condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Zd to that on Rd. Then,we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.

论文目录

文章来源

类型: 期刊论文

作者: 陈乐,Kunwoo KIM

来源: Acta Mathematica Scientia 2019年03期

年度: 2019

分类: 基础科学

专业: 数学

单位: Department of Mathematical Sciences, University of Nevada,Department of Mathematics, Pohang University of Science and Technology

基金: supported by the National Research Foundation of Korea (NRF-2017R1C1B1005436),the TJ Park Science Fellowship of POSCO TJ Park Foundation

分类号: O211.63

页码: 645-668

总页数: 24

文件大小: 420K

下载量: 8

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