The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise
2013 ed.
Book Details
Format
Paperback / Softback
Book Series
Lecture Notes in Mathematics
ISBN-10
3319008277
ISBN-13
9783319008271
Edition
2013 ed.
Publisher
Springer International Publishing AG
Imprint
Springer International Publishing AG
Country of Manufacture
CH
Country of Publication
GB
Publication Date
Oct 14th, 2013
Print length
165 Pages
Weight
290 grams
Dimensions
15.30 x 24.10 x 1.40 cms
Product Classification:
Differential calculus & equationsDifferential calculus and equations
Ksh 5,750.00
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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.
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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