Arnaud Debussche, Michael Högele, Peter Imkeller

The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise (eBook, PDF)

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 165
• Erscheinungstermin: 1. Oktober 2013
• Englisch
• ISBN-13: 9783319008288
• Artikelnr.: 43783289

Inhaltsangabe

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.