EAN: 9783319008271

THE DYNAMICS OF NONLINEAR REACTION-DIFFUSION EQ...

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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