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...
| Published in: | Springer eBooks |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham :
Springer International Publishing : Imprint: Springer,
2015.
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| Series: | SpringerBriefs in Mathematics,
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| Subjects: | |
| Online Access: | http://dx.doi.org/10.1007/978-3-319-12496-4 Перейти в каталог НБ ТГУ |
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| 100 | 1 | |a Chekroun, Mickaël D. |e author. |9 464606 | |
| 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. |
| 260 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2015. |9 742221 | ||
| 300 | |a XV, 127 p. 1 illus. in color. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8198 | |
| 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 mathematics. |9 566183 | |
| 650 | 0 | |a Dynamics. |9 460472 | |
| 650 | 0 | |a Ergodic theory. |9 461180 | |
| 650 | 0 | |a Differential Equations. |9 303496 | |
| 650 | 0 | |a Partial Differential Equations. |9 303602 | |
| 650 | 0 | |a Probabilities. |9 295556 | |
| 650 | 1 | 4 | |a Mathematics. |9 566184 |
| 650 | 2 | 4 | |a Dynamical Systems and Ergodic Theory. |9 303500 |
| 650 | 2 | 4 | |a Partial Differential Equations. |9 303602 |
| 650 | 2 | 4 | |a Probability Theory and Stochastic Processes. |9 303734 |
| 650 | 2 | 4 | |a Ordinary Differential Equations. |9 303501 |
| 700 | 1 | |a Liu, Honghu. |e author. |9 464607 | |
| 700 | 1 | |a Wang, Shouhong. |e author. |9 446369 | |
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| 856 | |y Перейти в каталог НБ ТГУ |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=413380 | ||
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