The dynamics of nonlinear reaction-diffusion equations with small Lévy noise [Documento electrónico] / Arnaud Debussche, Michael Högele, Peter Imkeller
Language: eng.Country: Germany.Publication: Cham : Springer International Publishing, 2013Description: XIV, 165 p. : il.ISBN: 978-3-319-00828-8.Series: Lecture Notes in MathematicsSubject - Topical Name: Equações diferenciais estocásticas | Processos de Lévy Online Resources:Click here to access onlineItem type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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E-Books | Biblioteca NOVA FCT Online | Não Ficção | QA274.25.SPR FCT 81841 (Browse shelf(Opens below)) | 1 | Available |
Colocação: Online
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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