The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise

• Main Authors: Debussche, Arnaud (Author), Högele, Michael (Author), Imkeller, Peter (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Series: Lecture Notes in Mathematics, 2085
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Partial differential equations.; Probabilities.; Probability Theory and Stochastic Processes.; Dynamical Systems and Ergodic Theory.; Partial Differential Equations.

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 deve...

Table of Contents:

• Introduction
• 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
• The source of stochastic models in conceptual climate dynamics.