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

著者: Arnaud Debussche
出版: Cham, Switzerland : Springer, ©2013.
シリーズ: Lecture notes in mathematics (Springer-Verlag), 2085.
エディション/フォーマット:   電子書籍 : Document : Englishすべてのエディションとフォーマットを見る
データベース:WorldCat
概要:
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  続きを読む
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ジャンル/形式: Electronic books
その他のフォーマット: Printed edition:
資料の種類: Document, インターネット資料
ドキュメントの種類: インターネットリソース, コンピューターファイル
すべての著者/寄与者: Arnaud Debussche
ISBN: 9783319008288 3319008285
OCLC No.: 859522804
物理形態: 1 online resource (xiii, 163 pages) : color illustrations.
コンテンツ: 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.
シリーズタイトル: Lecture notes in mathematics (Springer-Verlag), 2085.
責任者: Arnaud Debussche, Michael Högele, Peter Imkeller.

概要:

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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