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

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Description

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.
Release date NZ
October 14th, 2013
Audience
  • Postgraduate, Research & Scholarly
Illustrations
8 Illustrations, color; 1 Illustrations, black and white; XIV, 165 p. 9 illus., 8 illus. in color.
Pages
165
Dimensions
155x235x10
ISBN-13
9783319008271
Product ID
21401165

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