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008 130930s2013 gw | s |||| 0|eng d
020 _a9783319008288
_9978-3-319-00828-8
024 7 _a10.1007/978-3-319-00828-8
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aDebussche, Arnaud.
_eauthor.
245 1 4 _aThe Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise
_h[electronic resource] /
_cby Arnaud Debussche, Michael Högele, Peter Imkeller.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2013.
300 _aXIV, 165 p. 9 illus., 8 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2085
505 0 _aIntroduction -- 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 _aThis 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 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential equations, partial.
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aPartial Differential Equations.
700 1 _aHögele, Michael.
_eauthor.
700 1 _aImkeller, Peter.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319008271
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2085
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-00828-8
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c96482
_d96482