# The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise [electronic resource] / by Arnaud Debussche, Michael Högele, Peter Imkeller.

Series: Lecture Notes in Mathematics ; 2085Publisher: Cham : Springer International Publishing : Imprint: Springer, 2013Description: XIV, 165 p. 9 illus., 8 illus. in color. online resourceContent type:- text

- computer

- online resource

- 9783319008288

- 519.2 23

- QA273.A1-274.9
- QA274-274.9

Item type | Current library | Call number | Status | Date due | Barcode | |
---|---|---|---|---|---|---|

E-Books | Central Library, IISER Bhopal | 519.2 (Browse shelf(Opens below)) | Not for loan |

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.

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.

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