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

著者: Arnaud Debussche
出版商: Cham, Switzerland : Springer, ©2013.
丛书: Lecture notes in mathematics (Springer-Verlag), 2085.
版本/格式:   电子图书 : 文献 : 英语查看所有的版本和格式
数据库: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  再读一些...
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类型/形式: Electronic books
附加的形体格式: Printed edition:
材料类型: 文献, 互联网资源
文件类型: 互联网资源, 计算机文档
所有的著者/提供者: Arnaud Debussche
ISBN: 9783319008288 3319008285
OCLC号码: 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.
丛书名: Lecture notes in mathematics (Springer-Verlag), 2085.
责任: Arnaud Debussche, Michael Högele, Peter Imkeller.

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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