Cham, Switzerland
9783319008288
3319008285
1617-9692
Lecture notes in mathematics,
Printed edition:
Stochastic partial differential equations
Debussche
Arnaud
Arnaud Debussche
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Lévy processes
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Lecture notes in mathematics (Springer-Verlag) ;
Springer
2016-08-14
2013
en
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.
The dynamics of nonlinear reaction-diffusion equations with small lévy noise
859522804
859522804
2013