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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 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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  • "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."
  • "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."@en

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  • "Livre électronique (Descripteur de forme)"
  • "Electronic books"
  • "Llibres electrònics"
  • "Ressource Internet (Descripteur de forme)"
  • "Online-Publikation"

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  • "The dynamics of nonlinear reaction-diffusion equations with small Lévy noise"@en
  • "The dynamics of nonlinear reaction-diffusion equations with small Lévy noise"
  • "The dynamics of nonlinear reaction-diffusion equations with small lévy noise"
  • "The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Levy Noise"
  • "The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise"
  • "The Dynamics of nonlinear reaction-diffusion equations with small Lévy noise"