Series: Lecture Notes in Mathematics, Vol. 2085
Debussche, Arnaud, Högele, Michael, Imkeller, Peter
2013, XIV, 165 p. 9 illus., 8 illus. in color.
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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.
Content Level » Research
Keywords » Conceptual climate models - First exit problem - Metastability - Non-Gaussian Lévy noise - Stochastic nonlinear reaction-diffusion equations
Related subjects » Dynamical Systems & Differential Equations - Probability Theory and Stochastic Processes
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