The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lvy Noise |
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Author:
| Debussche, Arnaud Hgele, Michael Imkeller, Peter |
Series title: | Lecture Notes in Mathematics Ser. |
ISBN: | 978-3-319-00827-1 |
Publication Date: | Oct 2013 |
Publisher: | Springer International Publishing AG
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Imprint: | Springer |
Book Format: | Paperback |
List Price: | USD $49.99 |
Book Description:
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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...
More Description
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.