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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 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.
| Autorius: | Arnaud Debussche, Peter Imkeller, Michael Högele, |
| Serija: | Lecture Notes in Mathematics |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2013 |
| Knygos puslapių skaičius: | 180 |
| ISBN-10: | 3319008277 |
| ISBN-13: | 9783319008271 |
| Formatas: | 235 x 155 x 11 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise“
