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The dynamics of nonlinear reaction-diffusion equations with small lévy noise

Autor: Arnaud Debussche; SpringerLink (Online service)
Editora: Cham, Switzerland : Springer, ©2013.
Séries: Lecture notes in mathematics (Springer-Verlag), 2085.
Edição/Formato   e-book : Documento : InglêsVer todas as edições e formatos
Base de Dados:WorldCat
Resumo:
This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and  Ler mais...
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Detalhes

Tipo de Material: Documento, Recurso Internet
Tipo de Documento: Recurso Internet, Arquivo de Computador
Todos os Autores / Contribuintes: Arnaud Debussche; SpringerLink (Online service)
ISBN: 9783319008288 3319008285
Número OCLC: 859522804
Descrição: 1 online resource (xiii, 163 p.) : col. ill.
Conteúdos: The Fine Dynamics of the Chafee-Infante Equation --
The Stochastic Chafee-Infante Equation --
The Small Deviation of the Small Noise Solution --
Asymptotic Exit Times --
Asymptotic Transition Times --
Localization and Metastability.
Título da Série: Lecture notes in mathematics (Springer-Verlag), 2085.
Responsabilidade: Arnaud Debussche, Michael Högele, Peter Imkeller.
Mais informações:

Resumo:

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

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