TY  - BOOK
AU  - Debussche,Arnaud
AU  - Högele,Michael
AU  - Imkeller,Peter
ED  - SpringerLink (Online service)
TI  - The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
T2  - Lecture Notes in Mathematics,
SN  - 9783319008288
AV  - QA273.A1-274.9 
U1  - 519.2 23
PY  - 2013///
CY  - Cham
PB  - Springer International Publishing, Imprint: Springer
KW  - Mathematics
KW  - Differentiable dynamical systems
KW  - Differential equations, partial
KW  - Distribution (Probability theory)
KW  - Probability Theory and Stochastic Processes
KW  - Dynamical Systems and Ergodic Theory
KW  - Partial Differential Equations
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-319-00828-8
ER  -