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

Debussche, Arnaud; Högele, Michael; Imkeller, Peter

Couverture souple

ISBN 10 : 3319008277 ISBN 13 : 9783319008271

Editeur : Springer, 2013

Synopsis

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2013
• Langue: anglais
• ISBN 10: 3319008277
• ISBN 13: 9783319008271
• Reliure: Broché
• Nombre de pages: 180
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne