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The dynamics of nonlinear reaction-diffusion equations with small lévy noise Titelvorschau
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The dynamics of nonlinear reaction-diffusion equations with small lévy noise

Verfasser/in: Arnaud Debussche; SpringerLink (Online service)
Verlag: Cham, Switzerland : Springer, ©2013.
Serien: Lecture notes in mathematics (Springer-Verlag), 2085.
Ausgabe/Format   E-Book : Dokument : EnglischAlle Ausgaben und Formate anzeigen
Datenbank:WorldCat
Zusammenfassung:
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  Weiterlesen…
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Physisches Format Printed edition:
Medientyp: Dokument, Internetquelle
Dokumenttyp: Internet-Ressource, Computer-Datei
Alle Autoren: Arnaud Debussche; SpringerLink (Online service)
ISBN: 9783319008288 3319008285
OCLC-Nummer: 859522804
Beschreibung: 1 online resource (xiii, 163 p.) : col. ill.
Inhalt: 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.
Serientitel: Lecture notes in mathematics (Springer-Verlag), 2085.
Verfasserangabe: Arnaud Debussche, Michael Högele, Peter Imkeller.
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Abstract:

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.

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