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

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 metast...

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Detalles Bibliográficos
Autores principales:	Groisman, P., Saglietti, S., Saintier, N.
Formato:	JOUR
Materias:	Blow-up Metastability Random perturbations Stochastic partial differential equations Partial differential equations Random processes Stochastic systems Domain of attraction Metastabilities Reaction diffusion equations Stable equilibrium Stochastic partial differential equation Time averages Linear equations
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_03044149_v128_n5_p1558_Groisman
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_03044149_v128_n5_p1558_Groisman
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spelling	todo:paper_03044149_v128_n5_p1558_Groisman2023-10-03T15:20:39Z Metastability for small random perturbations of a PDE with blow-up Groisman, P. Saglietti, S. Saintier, N. Blow-up Metastability Random perturbations Stochastic partial differential equations Partial differential equations Random processes Stochastic systems Blow-up Domain of attraction Metastabilities Random perturbations Reaction diffusion equations Stable equilibrium Stochastic partial differential equation Time averages Linear equations 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. © 2017 Elsevier B.V. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03044149_v128_n5_p1558_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 Metastability Random perturbations Stochastic partial differential equations Partial differential equations Random processes Stochastic systems Blow-up Domain of attraction Metastabilities Random perturbations Reaction diffusion equations Stable equilibrium Stochastic partial differential equation Time averages Linear equations
spellingShingle	Blow-up Metastability Random perturbations Stochastic partial differential equations Partial differential equations Random processes Stochastic systems Blow-up Domain of attraction Metastabilities Random perturbations Reaction diffusion equations Stable equilibrium Stochastic partial differential equation Time averages Linear equations Groisman, P. Saglietti, S. Saintier, N. Metastability for small random perturbations of a PDE with blow-up
topic_facet	Blow-up Metastability Random perturbations Stochastic partial differential equations Partial differential equations Random processes Stochastic systems Blow-up Domain of attraction Metastabilities Random perturbations Reaction diffusion equations Stable equilibrium Stochastic partial differential equation Time averages Linear equations
description	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. © 2017 Elsevier B.V.
format	JOUR
author	Groisman, P. Saglietti, S. Saintier, N.
author_facet	Groisman, P. Saglietti, S. Saintier, N.
author_sort	Groisman, P.
title	Metastability for small random perturbations of a PDE with blow-up
title_short	Metastability for small random perturbations of a PDE with blow-up
title_full	Metastability for small random perturbations of a PDE with blow-up
title_fullStr	Metastability for small random perturbations of a PDE with blow-up
title_full_unstemmed	Metastability for small random perturbations of a PDE with blow-up
title_sort	metastability for small random perturbations of a pde with blow-up
url	http://hdl.handle.net/20.500.12110/paper_03044149_v128_n5_p1558_Groisman
work_keys_str_mv	AT groismanp metastabilityforsmallrandomperturbationsofapdewithblowup AT sagliettis metastabilityforsmallrandomperturbationsofapdewithblowup AT saintiern metastabilityforsmallrandomperturbationsofapdewithblowup
_version_	1782029587340853248

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

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