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130930s2013 gw | s |||| 0|eng d |
| 020 |
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|a 9783319008288
|9 978-3-319-00828-8
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| 024 |
7 |
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|a 10.1007/978-3-319-00828-8
|2 doi
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|a QA273.A1-274.9
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|a QA274-274.9
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|a PBT
|2 bicssc
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|a PBWL
|2 bicssc
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|a MAT029000
|2 bisacsh
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|a 519.2
|2 23
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|a Debussche, Arnaud.
|e author.
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|a The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lv̌y Noise
|c by Arnaud Debussche, Michael Hg̲ele, Peter Imkeller.
|h [electronic resource] /
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| 264 |
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2013.
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| 300 |
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|a XIII, 163 p. 9 illus., 8 illus. in color.
|b online resource.
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| 336 |
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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| 490 |
1 |
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|a Lecture Notes in Mathematics,
|v 2085
|x 0075-8434 ;
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| 505 |
0 |
# |
|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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| 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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| 650 |
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|a Mathematics.
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| 650 |
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|a Differentiable dynamical systems.
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| 650 |
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|a Differential equations, partial.
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| 650 |
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|a Distribution (Probability theory).
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| 650 |
1 |
4 |
|a Mathematics.
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| 650 |
2 |
4 |
|a Probability Theory and Stochastic Processes.
|
| 650 |
2 |
4 |
|a Dynamical Systems and Ergodic Theory.
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| 650 |
2 |
4 |
|a Partial Differential Equations.
|
| 700 |
1 |
# |
|a Hg̲ele, Michael.
|e author.
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| 700 |
1 |
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|a Imkeller, Peter.
|e author.
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer eBooks
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| 776 |
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8 |
|i Printed edition:
|z 9783319008271
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| 830 |
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|a Lecture Notes in Mathematics,
|v 2085
|x 0075-8434 ;
|
| 856 |
4 |
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|u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-319-00828-8
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| 912 |
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|a ZDB-2-SMA
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| 912 |
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|a ZDB-2-LNM
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
|