Metastability for small random perturbations of a PDE with blow-up

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Groisman, Pablo^1,2  Saglietti, Santiago^1,3  Saintier, Nicolas¹ 

[1] Univ Buenos Aires, FCEN, Dept Matemat, IMAS,CONICET, Buenos Aires, DF, Argentina

[2] NYU Shanghai, NYU ECNU Inst Math Sci, Shanghai, Peoples R China

[3] Technion, Fac Ind Engn & Management, Haifa, Israel

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

DOI  :  10.1016/j.spa.2017.08.005

来源: Elsevier

【 摘 要 】

We study random perturbations of a reaction-diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation epsilon > 0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in epsilon(-2)). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

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