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

저자: Arnaud Debussche
출판사: Cham, Switzerland : Springer, ©2013.
시리즈: Lecture notes in mathematics (Springer-Verlag), 2085.
판/형식:   전자도서 : 문서 : 영어모든 판과 형식 보기
데이터베이스:WorldCat
요약:
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  더 읽기…
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추가적인 물리적 형식: Printed edition:
자료 유형: 문서, 인터넷 자료
문서 형식: 인터넷 자원, 컴퓨터 파일
모든 저자 / 참여자: Arnaud Debussche
ISBN: 9783319008288 3319008285
OCLC 번호: 859522804
설명: 1 online resource (xiii, 163 pages) : color illustrations.
내용: 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.
일련 제목: Lecture notes in mathematics (Springer-Verlag), 2085.
책임: Arnaud Debussche, Michael Högele, Peter Imkeller.
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초록:

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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