The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise

1. Auflage 2013
ISBN: 978-3-319-00827-1
Verlag: Springer

Buch, Englisch, Band 2085, 165 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 2818 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Debussche, Arnaud

Högele, Michael

Imkeller, Peter

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

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.