The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise: 2085 (Lecture Notes in Mathematics, 2085) - Softcover

Debussche, Arnaud; Högele, Michael; Imkeller, Peter

Softcover

ISBN 10: 3319008277 ISBN 13: 9783319008271

Publisher: 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.

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From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2013
• Language: English
• ISBN 10: 3319008277
• ISBN 13: 9783319008271
• Binding: Paperback
• Number of pages: 179