Impacts of noise on a class of partial differential equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:258

Article

Lv, Guangying¹  Duan, Jinqiao² 

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

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

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

DOI  :  10.1016/j.jde.2014.12.002

来源: Elsevier

【 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.

【 授权许可】

Free