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 deve...
| Main Authors: | , , |
|---|---|
| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2013, 2013
|
| Edition: | 1st ed. 2013 |
| Series: | Lecture Notes in Mathematics
|
| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
| Summary: | 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 |
|---|---|
| Physical Description: | XIV, 165 p. 9 illus., 8 illus. in color online resource |
| ISBN: | 9783319008288 |