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＜電子ブック＞
The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise / by Arnaud Debussche, Michael Högele, Peter Imkeller
(Lecture Notes in Mathematics. ISSN:16179692 ; 2085)

版	1st ed. 2013.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2013
大きさ	XIV, 165 p. 9 illus., 8 illus. in color : online resource
著者標目	*Debussche, Arnaud author Högele, Michael author Imkeller, Peter author SpringerLink (Online service)
件　名	LCSH:Probabilities LCSH:Dynamical systems LCSH:Differential equations FREE:Probability Theory FREE:Dynamical Systems FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-00828-8

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