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

Arnaud Debussche

ISBN 10: 3319008277 / ISBN 13: 9783319008271

Published by Springer International Publishing, Springer International Publishing, 2013

About this Item

Druck auf Anfrage Neuware - Printed after ordering - 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.

Seller Inventory # 9783319008271

Bibliographic Details

• Title: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
• Publisher: Springer International Publishing, Springer International Publishing
• Publication Date: 2013
• Language: English
• ISBN 10: 3319008277
• ISBN 13: 9783319008271
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 235W x 155H x 11D millimeters 235 millimeters width by 155 millimeters height by 11 millimeters depth
• Weight: 283 grams

About this title

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.