The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Arnaud Debussche, Michael Högele, Peter Imkeller - The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Published: 2013-10-14 | ISBN: 3319008277 | PDF | 165 pages | 1 MB
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.