Explosive solutions of stochastic reaction-diffusion equations in mean Lp-norm

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Chow, Pao-Liu

关键词: Stochastic reaction-diffusion equation;    Ito's formula;    Positive solutions;    Blow-up of solutions;    Explosions;   

DOI  :  10.1016/j.jde.2010.11.008

来源: Elsevier

【 摘 要 】

The paper is concerned with the problem of non-existence of global solutions for a class of stochastic reaction-diffusion equations of Ito type. Under some sufficient conditions on the initial state, the nonlinear term and the multiplicative noise, it is proven that, in a bounded domain D subset of R-d, there exist positive solutions whose mean L-p-norm will blow up in finite time for p >= 1, while. if D = R-d, the previous result holds in any compact subset of R-d. Two examples are given to illustrate some application of the theorems. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free