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

Pablo Groisman, Santiago Saglietti and Nicolas Saintier

Stochastic Processes and their Applications, 2018, vol. 128, issue 5, 1558-1589

Abstract: 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 ε>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 ε−2). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution.

Keywords: Stochastic partial differential equations; Random perturbations; Blow-up; Metastability (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:5:p:1558-1589

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DOI: 10.1016/j.spa.2017.08.005

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