The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise

Arnaud Debussche

ISBN 10: 3319008277 / ISBN 13: 9783319008271

Editore: Springer International Publishing Okt 2013, 2013

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Neuware -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. 180 pp. Englisch.

Codice articolo 9783319008271

Dati bibliografici

• Titolo: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
• Editore: Springer International Publishing Okt 2013
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3319008277
• ISBN 13: 9783319008271
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 11 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 11 millimetri di profondità
• Peso: 283 grammi

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Riassunto

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.