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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise (Lecture Notes in Mathematics, 2085) - Softcover
Synopsis
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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From the Back Cover
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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THE DYNAMICS OF NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SMALL LÉVY NOISE
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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise (Lecture Notes in Mathematics, 2085)
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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise
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The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
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Springer International Publishing Okt 2013, 2013
ISBN 10: 3319008277
ISBN 13: 9783319008271
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Taschenbuch. Condition: Neu. 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. Seller Inventory # 9783319008271
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