Lecture Notes in Mathematics

Debussche, Arnaud; Högele, Michael; Imkeller, Peter

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.

Details

Published by: Springer

Publication Date: 2013-10-14

Format: Paperback

ISBN-13: 9783319008271

DOI: 10.1007/978-3-319-00828-8

Dimensions: 235cm x155cm

Pages: 165