Small Random Perturbations of a Dynamical System with Blow-up

Pablo Groisman; Santiago Saglietti

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arXiv · 1011.3414

Small Random Perturbations of a Dynamical System with Blow-up

Pablo Groisman·Santiago Saglietti

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Abstract

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.

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Pablo Groisman, Santiago Saglietti. 2010-11-15. Small Random Perturbations of a Dynamical System with Blow-up. https://arxiv.org/abs/1011.3414

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