The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise (Paperback, 2013 ed.)

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.

General

Imprint:	Springer International Publishing AG
Country of origin:	Switzerland
Series:	Lecture Notes in Mathematics, 2085
Release date:	October 2013
First published:	2013
Authors:	Arnaud Debussche • Michael Hoegele • Peter Imkeller
Dimensions:	235 x 155 x 14mm (L x W x T)
Format:	Paperback
Pages:	165
Edition:	2013 ed.
ISBN-13:	978-3-319-00827-1
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
LSN:	3-319-00827-7
Barcode:	9783319008271

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