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

Author: Arnaud Debussche
Publisher: Cham, Switzerland : Springer, ©2013.
Series: Lecture notes in mathematics (Springer-Verlag), 2085.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Arnaud Debussche
ISBN: 9783319008288 3319008285
OCLC Number: 859522804
Description: 1 online resource (xiii, 163 pages) : color illustrations.
Contents: 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.
Series Title: Lecture notes in mathematics (Springer-Verlag), 2085.
Responsibility: Arnaud Debussche, Michael Högele, Peter Imkeller.
More information:

Abstract:

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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