bokomslag The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lvy Noise
Vetenskap & teknik

The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lvy Noise

Arnaud Debussche Michael Hgele Peter Imkeller

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  • 165 sidor
  • 2013
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.
  • Författare: Arnaud Debussche, Michael Hgele, Peter Imkeller
  • Format: Pocket/Paperback
  • ISBN: 9783319008271
  • Språk: Engelska
  • Antal sidor: 165
  • Utgivningsdatum: 2013-10-14
  • Förlag: Springer International Publishing AG