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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise: Lecture Notes in Mathematics, cartea 2085

Autor Arnaud Debussche, Michael Högele, Peter Imkeller
en Limba Engleză Paperback – 14 oct 2013
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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Specificații

ISBN-13: 9783319008271
ISBN-10: 3319008277
Pagini: 180
Ilustrații: XIV, 165 p. 9 illus., 8 illus. in color.
Dimensiuni: 155 x 235 x 9 mm
Greutate: 0.28 kg
Ediția:2013
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

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.

Textul de pe ultima copertă

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.

Caracteristici

The comprehensive presentation serves as an excellent basis for a Master's course on stochastic partial differential equations(SPDEs) with Lévy noise The showcase character of this study provides particular insight into the methods developed and stimulates future research An additional chapter connects the mathematical results to its climatological motivation Includes supplementary material: sn.pub/extras