The Dynamics Of Nonlinear Reaction-diffusion Equations With Small Levy Noise by Arnaud DebusscheThe Dynamics Of Nonlinear Reaction-diffusion Equations With Small Levy Noise by Arnaud Debussche

The Dynamics Of Nonlinear Reaction-diffusion Equations With Small Levy Noise

byArnaud Debussche, Michael Högele, Peter Imkeller

Paperback | October 14, 2013

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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.

Title:The Dynamics Of Nonlinear Reaction-diffusion Equations With Small Levy NoiseFormat:PaperbackDimensions:165 pagesPublished:October 14, 2013Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319008277

ISBN - 13:9783319008271

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Table of Contents

Introduction.- 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.- The source of stochastic models in conceptual climate dynamics.