The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise /
Debussche, Arnaud.
The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise / by Arnaud Debussche, Michael Högele, Peter Imkeller. - xiv, 165 páginas 9 ilustraciones, 8 ilustraciones en color. recurso en línea. - Lecture Notes in Mathematics, 2085 0075-8434 ; .
Springer eBooks
Introduction -- The fine dynamics of the Chafee- Infante equation -- The stochastic Chafee- Infante equation -- The small deviation of the small noise solution -- Asymptotic exit times -- Asymptotic transition times -- Localization and metastability -- The source of stochastic models in conceptual climate dynamics.
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.
9783319008288
10.1007/9783319008288 doi
QA273.A1-274.9
The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise / by Arnaud Debussche, Michael Högele, Peter Imkeller. - xiv, 165 páginas 9 ilustraciones, 8 ilustraciones en color. recurso en línea. - Lecture Notes in Mathematics, 2085 0075-8434 ; .
Springer eBooks
Introduction -- The fine dynamics of the Chafee- Infante equation -- The stochastic Chafee- Infante equation -- The small deviation of the small noise solution -- Asymptotic exit times -- Asymptotic transition times -- Localization and metastability -- The source of stochastic models in conceptual climate dynamics.
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.
9783319008288
10.1007/9783319008288 doi
QA273.A1-274.9