The Dynamics Of Nonlinear Reactiondiffusion Equations With Small Lvy Noise 1st Edition Arnaud Debussche by Arnaud Debussche, Michael Högele, Peter Imkeller (auth.) 9783319008271, 9783319008288, 3319008277, 3319008285 instant download after payment.

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.