The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise Paperback / softback
Part of the Lecture Notes in Mathematics series
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.
- Format: Paperback / softback
- Pages: 165 pages, 8 Illustrations, color; 1 Illustrations, black and white; XIV, 165 p. 9 illus., 8 illus.
- Publisher: Springer International Publishing AG
- Publication Date: 01/10/2013
- Category: Differential calculus & equations
- ISBN: 9783319008271
- PDF from £27.19