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

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 deve...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Debussche, Arnaud (Autor), Högele, Michael (Autor), Imkeller, Peter (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2013.
Edición:1st ed. 2013.
Colección:Lecture Notes in Mathematics, 2085
Temas:
Probabilities.
Dynamical systems.
Differential equations.
Probability Theory.
Dynamical Systems.
Differential Equations.
Acceso en línea:Texto Completo

MARC

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100 1 |a Debussche, Arnaud.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 4 |a The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise  |h [electronic resource] /  |c by Arnaud Debussche, Michael Högele, Peter Imkeller. 
250 |a 1st ed. 2013. 
264 1 |a Cham :  |b Springer International Publishing :  |b Imprint: Springer,  |c 2013. 
300 |a XIV, 165 p. 9 illus., 8 illus. in color.  |b online resource. 
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490 1 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2085 
505 0 |a 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. 
520 |a 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. 
650 0 |a Probabilities. 
650 0 |a Dynamical systems. 
650 0 |a Differential equations. 
650 1 4 |a Probability Theory. 
650 2 4 |a Dynamical Systems. 
650 2 4 |a Differential Equations. 
700 1 |a Högele, Michael.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
700 1 |a Imkeller, Peter.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
773 0 |t Springer Nature eBook 
776 0 8 |i Printed edition:  |z 9783319008271 
776 0 8 |i Printed edition:  |z 9783319008295 
830 0 |a Lecture Notes in Mathematics,  |x 1617-9692 ;  |v 2085 
856 4 0 |u https://doi.uam.elogim.com/10.1007/978-3-319-00828-8  |z Texto Completo 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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