東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Approximation of stochastic invarian...

Chekroun, Mickael D.

Linked to FindBook

Google Book

Amazon

博客來

Approximation of stochastic invariant manifolds = stochastic manifolds for nonlinear SPDEs I /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Approximation of stochastic invariant manifolds/ by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
Reminder of title:	stochastic manifolds for nonlinear SPDEs I /
Author:	Chekroun, Mickael D.
other author:	Liu, Honghu.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	xv, 127 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Stochastic partial differential equations. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-12496-4
ISBN:	9783319124964 (electronic bk.)

Approximation of stochastic invariant manifolds = stochastic manifolds for nonlinear SPDEs I /
Chekroun, Mickael D.

Approximation of stochastic invariant manifoldsstochastic manifolds for nonlinear SPDEs I /[electronic resource] :by Mickael D. Chekroun, Honghu Liu, Shouhong Wang. - Cham :Springer International Publishing :2015. - xv, 127 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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.

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.

ISBN: 9783319124964 (electronic bk.)

Standard No.: 10.1007/978-3-319-12496-4doiSubjects--Topical Terms:

625093
Stochastic partial differential equations.

LC Class. No.: QA274.25

Dewey Class. No.: 515.353

Approximation of stochastic invariant manifolds = stochastic manifolds for nonlinear SPDEs I /
LDR:02893nmm a2200325 a 4500 001 1994637
003 DE-He213
005 20150812131957.0
006 m d
007 cr nn 008maaau
008 151019s2015 gw s 0 eng d
020 $a 9783319124964 (electronic bk.)
020 $a 9783319124957 (paper)
024 7 $a 10.1007/978-3-319-12496-4 $2 doi
035 $a 978-3-319-12496-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.25
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
082 0 4 $a 515.353 $2 23
090 $a QA274.25 $b .C515 2015
100 1 $a Chekroun, Mickael D. $3 2133571
245 1 0 $a Approximation of stochastic invariant manifolds $h [electronic resource] : $b stochastic manifolds for nonlinear SPDEs I / $c by Mickael D. Chekroun, Honghu Liu, Shouhong Wang.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a xv, 127 p. : $b ill., digital ; $c 24 cm.
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 Stochastic partial differential equations. $3 625093
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Dynamical Systems and Ergodic Theory. $3 891276
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Probability Theory and Stochastic Processes. $3 891080
650 2 4 $a Ordinary Differential Equations. $3 891264
700 1 $a Liu, Honghu. $3 2133572
700 1 $a Wang, Shouhong. $3 935654
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-12496-4
950 $a Mathematics and Statistics (Springer-11649)