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141220s2015 gw | s |||| 0|eng d |
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|a 9783319124964
|9 978-3-319-12496-4
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|a 10.1007/978-3-319-12496-4
|2 doi
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|a Chekroun, Mickaël D.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Approximation of Stochastic Invariant Manifolds
|h [electronic resource] :
|b Stochastic Manifolds for Nonlinear SPDEs I /
|c by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang.
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| 250 |
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|a 1st ed. 2015.
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| 264 |
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1 |
|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2015.
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| 300 |
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|a XV, 127 p. 1 illus. in color.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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|a SpringerBriefs in Mathematics,
|x 2191-8198
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|a General Introduction -- Stochastic Invariant Manifolds: Background and Main Contributions -- Preliminaries -- Stochastic Evolution Equations -- Random Dynamical Systems -- Cohomologous Cocycles and Random Evolution Equations -- Linearized Stochastic Flow and Related Estimates -- Existence and Attraction Properties of Global Stochastic Invariant Manifolds -- Existence and Smoothness of Global Stochastic Invariant Manifolds -- Asymptotic Completeness of Stochastic Invariant Manifolds -- Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds -- Local Stochastic Critical Manifolds: Existence and Approximation Formulas -- Standing Hypotheses -- Existence of Local Stochastic Critical Manifolds -- Approximation of Local Stochastic Critical Manifolds -- Proofs of Theorem 6.1 and Corollary 6.1 -- Approximation of Stochastic Hyperbolic Invariant Manifolds -- A Classical and Mild Solutions of the Transformed RPDE -- B Proof of Theorem 4.1 -- References.
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| 520 |
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|a This first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems.
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|a Dynamics.
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|a Ergodic theory.
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|a Partial differential equations.
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|a Probabilities.
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| 650 |
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|a Differential equations.
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| 650 |
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|a Dynamical Systems and Ergodic Theory.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
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| 650 |
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|a Partial Differential Equations.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12155
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| 650 |
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|a Probability Theory and Stochastic Processes.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M27004
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| 650 |
2 |
4 |
|a Ordinary Differential Equations.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12147
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| 700 |
1 |
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|a Liu, Honghu.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 700 |
1 |
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|a Wang, Shouhong.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer Nature eBook
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| 776 |
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|i Printed edition:
|z 9783319124971
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| 776 |
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8 |
|i Printed edition:
|z 9783319124957
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| 830 |
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|a SpringerBriefs in Mathematics,
|x 2191-8198
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-319-12496-4
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| 912 |
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|a ZDB-2-SMA
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| 912 |
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|a ZDB-2-SXMS
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| 950 |
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|a Mathematics and Statistics (SpringerNature-11649)
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| 950 |
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|a Mathematics and Statistics (R0) (SpringerNature-43713)
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