Impacts of noise on a class of partial differential equations

被引：28

作者：

Lv, Guangying ^{[1
]}

Duan, Jinqiao ^{[2
]}

机构：

[1] Henan Univ, Inst Contemporary Math, Kaifeng 475001, Henan, Peoples R China

[2] IIT, Dept Appl Math, Chicago, IL 60616 USA

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 258卷 / 06期

关键词：

Ito's formula; Blow-up; Stochastic parabolic partial differential equation; Finite time singularity; Impact of noise; EXISTENCE;

D O I：

10.1016/j.jde.2014.12.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positive solution for a class of stochastic partial differential equations. Then, we prove that noise could induce singularities (finite time blow up of solutions). Finally, we show that a stochastic Allen-Cahn equation does not have finite time singularities and the unique solution exists globally. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：2196 / 2220

页数：25

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