The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
By: and and
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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.
- Copyright:
- 2013
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783319008288
- Publisher:
- Springer International Publishing, Cham
- Date of Addition:
- 10/14/16
- Copyrighted By:
- Springer
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.