TY - ELEC
DB - /z-wcorg/
DP - http://worldcat.org
ID - 859522804
LA - English
UR - http://link.springer.com/book/10.1007/978-3-319-00828-8
T1 - The dynamics of nonlinear reaction-diffusion equations with small lévy noise
AU - Debussche, Arnaud.
AU - SpringerLink (Online service)
PB - Springer
CY - Cham, Switzerland
Y1 - 2013///
SN - 9783319008288 3319008285
AB - 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.
ER -