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

• Κύριοι συγγραφείς: Debussche, Arnaud (Συγγραφέας), Högele, Michael (Συγγραφέας), Imkeller, Peter (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Springer, 2013.
• Σειρά: Lecture Notes in Mathematics, 2085
• Θέματα: 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 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. 

 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.