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 deve...
Main Authors: | , , |
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Format: | eBook |
Language: | English |
Published: |
Cham
Springer International Publishing
2013, 2013
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Edition: | 1st ed. 2013 |
Series: | Lecture Notes in Mathematics
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Subjects: | |
Online Access: | |
Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Summary: | 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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Physical Description: | XIV, 165 p. 9 illus., 8 illus. in color online resource |
ISBN: | 9783319008288 |