Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise
Peter Imkeller, Michael Hogele, Arnaud Debussche
E-bok
2013505 kr
Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
AvArnaud Debussche,Michael Högele
Häftad, Engelska, 2013
Del 2085 i serien Lecture Notes in Mathematics
390 kr
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Beskrivning
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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