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Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise

Name: Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise
Brand: Springer International Publishing AG
SKU: 01469014
Price: 35.98 EUR
Availability: InStock
Author: Arnaud Debussche
ISBN: 9783319008271

Arnaud Debussche

Michael Högele

Peter Imkeller

Language

English

Book Paperback

Libristo code: 01469014

Publishers Springer International Publishing AG, October 2013

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusi... Full description

Libristo code: 01469014

88 b

35.98 €

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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.