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.
- ISBN10 3319008293
- ISBN13 9783319008295
- Publish Date 30 September 2013
- Publish Status Withdrawn
- Out of Print 18 October 2014
- Publish Country US
- Imprint Springer
- Format Paperback (US Trade)
- Pages 180
- Language English