Click Here to Download: https://ouo.io/Bs6P4c The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise By: Arnaud Debussche; Michael Högele; Peter Imkeller Publisher: Springer Print ISBN: 9783319008271, 3319008277 eText ISBN: 9783319008288, 3319008285 Copyright year: 2013 Format: EPUB Available from $ 49.99 USD SKU 9783319008288 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.
