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Beschreibung
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.
Details
| Verlag | Springer International Publishing |
| Ersterscheinung | 14. Oktober 2013 |
| Maße | 23.5 cm x 15.5 cm |
| Gewicht | 283 Gramm |
| Format | Softcover |
| ISBN-13 | 9783319008271 |
| Seiten | 165 |
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