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The dynamics of nonlinear reaction-diffusion equations with small Lévy noise
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 deve...
Autores principales: | , , |
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Lenguaje: | eng |
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Springer
2013
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Acceso en línea: | https://dx.doi.org/10.1007/978-3-319-00828-8 http://cds.cern.ch/record/1690661 |
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author | Debussche, Arnaud Högele, Michael Imkeller, Peter |
author_facet | Debussche, Arnaud Högele, Michael Imkeller, Peter |
author_sort | Debussche, Arnaud |
collection | CERN |
description | 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. |
id | cern-1690661 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2013 |
publisher | Springer |
record_format | invenio |
spelling | cern-16906612021-04-21T21:14:13Zdoi:10.1007/978-3-319-00828-8http://cds.cern.ch/record/1690661engDebussche, ArnaudHögele, MichaelImkeller, PeterThe dynamics of nonlinear reaction-diffusion equations with small Lévy noiseMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:16906612013 |
spellingShingle | Mathematical Physics and Mathematics Debussche, Arnaud Högele, Michael Imkeller, Peter The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title_full | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title_fullStr | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title_full_unstemmed | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title_short | The dynamics of nonlinear reaction-diffusion equations with small Lévy noise |
title_sort | dynamics of nonlinear reaction-diffusion equations with small lévy noise |
topic | Mathematical Physics and Mathematics |
url | https://dx.doi.org/10.1007/978-3-319-00828-8 http://cds.cern.ch/record/1690661 |
work_keys_str_mv | AT debusschearnaud thedynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise AT hogelemichael thedynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise AT imkellerpeter thedynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise AT debusschearnaud dynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise AT hogelemichael dynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise AT imkellerpeter dynamicsofnonlinearreactiondiffusionequationswithsmalllevynoise |