Small random perturbations of a dynamical system with blow-up

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Groisman, Pablo¹  Saglietti, Santiago¹ 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Buenos Aires, DF, Argentina

关键词: Random perturbations;    Explosions;    Stochastic differential equations;    Blow-up;    Metastability;   

DOI  :  10.1016/j.jmaa.2011.06.034

来源: Elsevier

【 摘 要 】

We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free