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

von Arnaud Debussche, Michael Högele, Peter Imkeller

165 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783319008271
• Sprache: Englisch
• Erscheinungsdatum: 14.10.2013
• Genre: Mathematik/Wahrscheinlichkeitstheorie, Stochastik, Mathematische Statistik
• Verlag: Springer International Publishing