Authors:
The comprehensive presentation serves as an excellent basis for a Master's course on stochastic partial differential equations(SPDEs) with Lévy noise
The showcase character of this study provides particular insight into the methods developed and stimulates future research
An additional chapter connects the mathematical results to its climatological motivation
Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2085)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
Keywords
- Conceptual climate models
- First exit problem
- Metastability
- Non-Gaussian Lévy noise
- Stochastic nonlinear reaction-diffusion equations
- partial differential equations
Authors and Affiliations
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Ecole Normale Supérieure Cachan Antenne de Bretagne, Bruz, Rennes, France
Arnaud Debussche
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Institut für Mathematik LS Wahrscheinlichkeitstheorie, Universität Potsdam, Potsdam, Germany
Michael Högele
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Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany
Peter Imkeller
Bibliographic Information
Book Title: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
Authors: Arnaud Debussche, Michael Högele, Peter Imkeller
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-319-00828-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2013
Softcover ISBN: 978-3-319-00827-1Published: 14 October 2013
eBook ISBN: 978-3-319-00828-8Published: 01 October 2013
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIV, 165
Number of Illustrations: 1 b/w illustrations, 8 illustrations in colour
Topics: Probability Theory, Dynamical Systems, Differential Equations