The Fine Dynamics of the Chafee-Infante Equation -- The Stochastic Chafee-Infante Equation -- The Small Deviation of the Small Noise Solution -- Asymptotic Exit Times -- Asymptotic Transition Times -- Localization and Metastability

Includes bibliographical references and index

Description based on online resource; title from PDF title page (SpringerLink, viewed Oct. 7, 2013)

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