The Dynamics Of Nonlinear Reaction Diffusion Equations With Small Levy Noise
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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Author | : Arnaud Debussche |
Publisher | : Springer |
Total Pages | : 175 |
Release | : 2013-10-01 |
Genre | : Mathematics |
ISBN | : 3319008285 |
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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.
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