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

Debussche, Arnaud; Högele, Michael; Imkeller, Peter

ISBN 10: 3319008277 / ISBN 13: 9783319008271

Editore: Springer, 2013

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Titolo: The Dynamics of Nonlinear Reaction-Diffusion...

Casa editrice: Springer

Data di pubblicazione: 2013

Legatura: Brossura

Condizione: New

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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.