Small random perturbations of a dynamical system with blow-up
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 as...
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Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v385_n1_p150_Groisman http://hdl.handle.net/20.500.12110/paper_0022247X_v385_n1_p150_Groisman |
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paper:paper_0022247X_v385_n1_p150_Groisman2023-06-08T14:47:54Z Small random perturbations of a dynamical system with blow-up Groisman, Pablo Jose Blow-up Explosions Metastability Random perturbations Stochastic differential equations 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. © 2011 Elsevier Inc. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v385_n1_p150_Groisman http://hdl.handle.net/20.500.12110/paper_0022247X_v385_n1_p150_Groisman |
institution |
Universidad de Buenos Aires |
institution_str |
I-28 |
repository_str |
R-134 |
collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
topic |
Blow-up Explosions Metastability Random perturbations Stochastic differential equations |
spellingShingle |
Blow-up Explosions Metastability Random perturbations Stochastic differential equations Groisman, Pablo Jose Small random perturbations of a dynamical system with blow-up |
topic_facet |
Blow-up Explosions Metastability Random perturbations Stochastic differential equations |
description |
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. © 2011 Elsevier Inc. |
author |
Groisman, Pablo Jose |
author_facet |
Groisman, Pablo Jose |
author_sort |
Groisman, Pablo Jose |
title |
Small random perturbations of a dynamical system with blow-up |
title_short |
Small random perturbations of a dynamical system with blow-up |
title_full |
Small random perturbations of a dynamical system with blow-up |
title_fullStr |
Small random perturbations of a dynamical system with blow-up |
title_full_unstemmed |
Small random perturbations of a dynamical system with blow-up |
title_sort |
small random perturbations of a dynamical system with blow-up |
publishDate |
2012 |
url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v385_n1_p150_Groisman http://hdl.handle.net/20.500.12110/paper_0022247X_v385_n1_p150_Groisman |
work_keys_str_mv |
AT groismanpablojose smallrandomperturbationsofadynamicalsystemwithblowup |
_version_ |
1768542113692123136 |