Small random perturbations of a dynamical system with blow-up

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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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Autores principales: Groisman, P., Saglietti, S.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2012
Materias:
Blow-up
Explosions
Metastability
Random perturbations
Stochastic differential equations
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v385_n1_p150_Groisman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_0022247X_v385_n1_p150_Groisman
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spelling paperaa:paper_0022247X_v385_n1_p150_Groisman2023-06-12T16:44:12Z Small random perturbations of a dynamical system with blow-up J. Math. Anal. Appl. 2012;385(1):150-166 Groisman, P. Saglietti, S. 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 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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)
language Inglés
orig_language_str_mv eng
topic Blow-up
Explosions
Metastability
Random perturbations
Stochastic differential equations
spellingShingle Blow-up
Explosions
Metastability
Random perturbations
Stochastic differential equations
Groisman, P.
Saglietti, S.
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.
format Artículo
Artículo
publishedVersion
author Groisman, P.
Saglietti, S.
author_facet Groisman, P.
Saglietti, S.
author_sort Groisman, P.
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 http://hdl.handle.net/20.500.12110/paper_0022247X_v385_n1_p150_Groisman
work_keys_str_mv AT groismanp smallrandomperturbationsofadynamicalsystemwithblowup
AT sagliettis smallrandomperturbationsofadynamicalsystemwithblowup
_version_ 1769810275076145152

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