The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise (Lecture Notes in Mathematics, 2085)
Language: English
Published by Springer, 2013
- Softcover
- New
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- Title
- The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise (Lecture Notes in Mathematics, 2085)
- Author
- Debussche, Arnaud; Högele, Michael; Imkeller, Peter
- Publisher
- Springer
- Publication year
- 2013
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 3319008277
- ISBN 13
- 9783319008271
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.
"Synopsis" may belong to another edition of this title.
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.
"About the title" may belong to another edition of this title.
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