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

Name: The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lvy Noise
Brand: Springer Nature
SKU: 9783319008271
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Springer Nature

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9783319008271

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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.

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