UID:
almahu_9947363766702882
Umfang:
XIV, 165 p. 9 illus., 8 illus. in color.
,
online resource.
ISBN:
9783319008288
Serie:
Lecture Notes in Mathematics, 2085
Inhalt:
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.
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9783319008271
Sprache:
Englisch
DOI:
10.1007/978-3-319-00828-8
URL:
http://dx.doi.org/10.1007/978-3-319-00828-8
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