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131001 ||| eng |
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|a 9783319008288
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|a Debussche, Arnaud
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| 245 |
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|a The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
|h Elektronische Ressource
|c by Arnaud Debussche, Michael Högele, Peter Imkeller
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| 250 |
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|a 1st ed. 2013
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| 260 |
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|a Cham
|b Springer International Publishing
|c 2013, 2013
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| 300 |
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|a XIV, 165 p. 9 illus., 8 illus. in color
|b online resource
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| 505 |
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|a Introduction -- The fine dynamics of the Chafee- Infante equation -- The stochastic Chafee- Infante equation -- The small deviation of the small noise solution -- Asymptotic exit times -- Asymptotic transition times -- Localization and metastability -- The source of stochastic models in conceptual climate dynamics
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| 653 |
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|a Dynamical Systems and Ergodic Theory
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| 653 |
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|a Ergodic theory
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| 653 |
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|a Partial Differential Equations
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| 653 |
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|a Partial differential equations
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| 653 |
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|a Probability Theory and Stochastic Processes
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| 653 |
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|a Probabilities
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| 653 |
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|a Dynamics
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| 700 |
1 |
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|a Högele, Michael
|e [author]
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| 700 |
1 |
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|a Imkeller, Peter
|e [author]
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Lecture Notes in Mathematics
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-319-00828-8?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
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|a 519.2
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| 520 |
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|a 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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