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The dynamics of nonlinear reaction-diffusion equations with small lévy noise

作者: Arnaud Debussche
出版商: Cham, Switzerland : Springer, ©2013.
叢書: Lecture notes in mathematics (Springer-Verlag), 2085.
版本/格式:   電子書 : 文獻 : 英語所有版本和格式的總覽
資料庫:WorldCat
提要:
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  再讀一些...
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其他的實體格式: Printed edition:
資料類型: 文獻, 網際網路資源
文件類型: 網路資源, 電腦資料
所有的作者/貢獻者: Arnaud Debussche
ISBN: 9783319008288 3319008285
OCLC系統控制編碼: 859522804
描述: 1 online resource (xiii, 163 pages) : color illustrations.
内容: 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.
叢書名: Lecture notes in mathematics (Springer-Verlag), 2085.
責任: Arnaud Debussche, Michael Högele, Peter Imkeller.
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摘要:

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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