The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
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.
| Autor: | Debussche, Arnaud Högele, Michael Imkeller, Peter |
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| ISBN: | 9783319008271 |
| Sprache: | Englisch |
| Seitenzahl: | 165 |
| Produktart: | Kartoniert / Broschiert |
| Verlag: | Springer International Publishing |
| Veröffentlicht: | 14.10.2013 |
| Schlagworte: | Conceptual climate models First exit problem Metastability Non-Gaussian Lévy noise Stochastic nonlinear reaction-diffusion equations partial differential equations |