The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
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| Verlag | Springer |
| Auflage | 2013 |
| Seiten | 165 |
| Format | 15,6 x 1,1 x 23,4 cm |
| Gewicht | 280 g |
| Artikeltyp | Englisches Buch |
| Reihe | Lecture Notes in Mathematics 2085 |
| ISBN-10 | 3319008277 |
| EAN | 9783319008271 |
| Bestell-Nr | 31900827A |
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.
Inhaltsverzeichnis:
Introduction.- The fine dynamics of the Chafee- Infante equation.- The stochastic Chafee- Infante equation.- The small deviation of the small noise solution.- Asymptotic exit times.- Asymptotic transition times.- Localization and metastability.- The source of stochastic models in conceptual climate dynamics.