LEADER 04788nam 22007695 450 001 9910299760903321 005 20251116140242.0 010 $a3-319-12496-X 024 7 $a10.1007/978-3-319-12496-4 035 $a(CKB)3710000000321548 035 $a(EBL)1966835 035 $a(OCoLC)898892853 035 $a(SSID)ssj0001408178 035 $a(PQKBManifestationID)11797470 035 $a(PQKBTitleCode)TC0001408178 035 $a(PQKBWorkID)11346218 035 $a(PQKB)10381786 035 $a(DE-He213)978-3-319-12496-4 035 $a(MiAaPQ)EBC1966835 035 $a(PPN)183150481 035 $a(EXLCZ)993710000000321548 100 $a20141220d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApproximation of stochastic invariant manifolds $estochastic manifolds for nonlinear SPDEs I /$fby Mickaël D. Chekroun, Honghu Liu, Shouhong Wang 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (136 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 08$a3-319-12495-1 320 $aIncludes bibliographical references and index. 327 $aGeneral 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. 330 $aThis first volume is concerned with the analytic derivation of explicit formulas for the leading-order Taylor approximations of (local) stochastic invariant manifolds associated with a broad class of nonlinear stochastic partial differential equations. These approximations  take the form of Lyapunov-Perron integrals, which are further characterized in Volume II as pullback limits associated with some partially coupled backward-forward systems. This pullback characterization provides a useful interpretation of the corresponding approximating manifolds and leads to a simple framework that unifies some other approximation approaches in the literature. A self-contained survey is also included on the existence and attraction of one-parameter families of stochastic invariant manifolds, from the point of view of the theory of random dynamical systems. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aDynamics 606 $aErgodic theory 606 $aDifferential equations, Partial 606 $aProbabilities 606 $aDifferential equations 606 $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 615 0$aDynamics. 615 0$aErgodic theory. 615 0$aDifferential equations, Partial. 615 0$aProbabilities. 615 0$aDifferential equations. 615 14$aDynamical Systems and Ergodic Theory. 615 24$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 615 24$aOrdinary Differential Equations. 676 $a510 676 $a515.352 676 $a515.353 676 $a515.39 700 $aChekroun$b Mickae?l D.$4aut$4http://id.loc.gov/vocabulary/relators/aut$00 702 $aLiu$b Honghu$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aWang$b Shouhong$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910299760903321 996 $aApproximation of Stochastic Invariant Manifolds$92499255 997 $aUNINA