Approximation of stochastic invariant manifolds : stochastic manifolds for nonlinear SPDEs I /
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| Author / Creator: | Chekroun, Mickaël D., author. |
|---|---|
| Imprint: | Cham, Switzerland : Springer, [2014] ©2015 |
| Description: | 1 online resource (xv, 127 pages) : color illustration. |
| Language: | English |
| Series: | SpringerBriefs in Mathematics, 2191-8198 SpringerBriefs in mathematics. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11091075 |
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| 100 | 1 | |a Chekroun, Mickaël D., |e author. |0 http://id.loc.gov/authorities/names/no2015125612 |1 http://viaf.org/viaf/213334251 | |
| 245 | 1 | 0 | |a Approximation of stochastic invariant manifolds : |b stochastic manifolds for nonlinear SPDEs I / |c Mickaël D. Chekroun, Honghu Liu, Shouhong Wang. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2014] | |
| 264 | 4 | |c ©2015 | |
| 300 | |a 1 online resource (xv, 127 pages) : |b color illustration. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
| 337 | |a computer |b c |2 rdamedia |0 http://id.loc.gov/vocabulary/mediaTypes/c | ||
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| 490 | 1 | |a SpringerBriefs in Mathematics, |x 2191-8198 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed January 7, 2015). | |
| 505 | 0 | |a Preface; Acknowledgments; Contents; Acronyms; 1 General Introduction; 2 Stochastic Invariant Manifolds: Background and Main Contributions; 3 Preliminaries; 3.1 Stochastic Evolution Equations; 3.2 Random Dynamical Systems; 3.3 Cohomologous Cocycles and Random Evolution Equations; 3.4 Linearized Stochastic Flow and Related Estimates; 4 Existence and Attraction Properties of Global Stochastic Invariant Manifolds; 4.1 Existence and Smoothness of Global Stochastic Invariant Manifolds; 4.2 Asymptotic Completeness of Stochastic Invariant Manifolds. | |
| 505 | 8 | |a 5 Local Stochastic Invariant Manifolds: Preparation to Critical Manifolds6 Local Stochastic Critical Manifolds: Existence and Approximation Formulas; 6.1 Standing Hypotheses; 6.2 Existence of Local Stochastic Critical Manifolds; 6.3 Approximation of Local Stochastic Critical Manifolds; 6.4 Proofs of Theorem 6.1 and Corollary 6.1; 7 Approximation of Stochastic Hyperbolic Invariant Manifolds; Appendix AClassical and Mild Solutionsof the Transformed RPDE; Appendix BProof of Theorem 4.1; References; Index. | |
| 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 unifie. | ||
| 650 | 0 | |a Stochastic partial differential equations. |0 http://id.loc.gov/authorities/subjects/sh87001697 | |
| 650 | 1 | 2 | |a Mathematics. |
| 650 | 1 | 2 | |a Probability. |
| 650 | 1 | 2 | |a Stochastic Processes. |
| 650 | 4 | |a Differentiable dynamical systems. | |
| 650 | 4 | |a Differential Equations. | |
| 650 | 4 | |a Differential equations, partial. | |
| 650 | 4 | |a Distribution (Probability theory. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Stochastic partial differential equations. |2 fast |0 (OCoLC)fst01133516 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Liu, Honghu, |e author. |0 http://id.loc.gov/authorities/names/no2012153350 |1 http://viaf.org/viaf/294689262 | |
| 700 | 1 | |a Wang, Shouhong, |e author. |0 http://id.loc.gov/authorities/names/n99024000 |1 http://viaf.org/viaf/81024656 | |
| 776 | 0 | 8 | |i Print version: |a Chekroun, Micka©"l D. |t Approximation of Stochastic Invariant Manifolds : Stochastic Manifolds for Nonlinear SPDEs I. |d Cham : Springer International Publishing, ©2014 |z 9783319124957 |
| 830 | 0 | |a SpringerBriefs in mathematics. |0 http://id.loc.gov/authorities/names/no2011133396 | |
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