The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
(Sprache: Englisch)
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...
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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.
Klappentext zu „The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise “
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.Inhaltsverzeichnis zu „The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise “
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.Bibliographische Angaben
- Autoren: Arnaud Debussche , Michael Högele , Peter Imkeller
- 2013, 2013, XIV, 165 Seiten, 8 farbige Abbildungen, Masse: 15,6 x 23,4 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3319008277
- ISBN-13: 9783319008271
Sprache:
Englisch
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