The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Peter Imkeller author Arnaud Debussche author Michael Högele author
Format:Paperback
Publisher:Springer International Publishing AG
Published:14th Oct '13
Currently unavailable, and unfortunately no date known when it will be back
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.
ISBN: 9783319008271
Dimensions: unknown
Weight: 2818g
165 pages
2013 ed.