The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise

Arnaud Debussche Michael Hogele Peter Imkeller

ISBN 10: 3319008277 / ISBN 13: 9783319008271

Published by Springer, 2013

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pp. 180. Seller Inventory # 2651413484

Bibliographic Details

Title: The Dynamics of Nonlinear Reaction-Diffusion...

Publisher: Springer

Publication Date: 2013

Binding: Soft cover

Condition: New

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Synopsis:

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.