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Approximation of Stochastic Invariant Manifolds Stochastic Manifolds for Nonlinear SPDEs I /
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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Edición: | 1st ed. 2015. |
| Colección: | SpringerBriefs in Mathematics,
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| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 008 | 141220s2015 sz | s |||| 0|eng d | ||
| 020 | |a 9783319124964 |9 978-3-319-12496-4 | ||
| 024 | 7 | |a 10.1007/978-3-319-12496-4 |2 doi | |
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| 082 | 0 | 4 | |a 515.39 |2 23 |
| 100 | 1 | |a Chekroun, Mickaël D. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |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. |
| 250 | |a 1st ed. 2015. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. | |
| 300 | |a XV, 127 p. 1 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8201 | |
| 505 | 0 | |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. | |
| 520 | |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. | ||
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 1 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Probability Theory. |
| 700 | 1 | |a Liu, Honghu. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 700 | 1 | |a Wang, Shouhong. |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 9783319124971 |
| 776 | 0 | 8 | |i Printed edition: |z 9783319124957 |
| 830 | 0 | |a SpringerBriefs in Mathematics, |x 2191-8201 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-319-12496-4 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
| 912 | |a ZDB-2-SXMS | ||
| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||