Effective dynamics of stochastic partial differential equations / (Record no. 246889)
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| fixed length control field | 06168cam a2200589Mi 4500 |
| 001 - CONTROL NUMBER | |
| control field | ocn872989896 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20190328114807.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr ||||||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 140224s2014 ne o 000 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | UKMGB |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | UKMGB |
| Modifying agency | OCLCO |
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| 016 7# - NATIONAL BIBLIOGRAPHIC AGENCY CONTROL NUMBER | |
| Record control number | 016651344 |
| Source | Uk |
| 019 ## - | |
| -- | 874322618 |
| -- | 880316058 |
| -- | 880408011 |
| -- | 968098901 |
| -- | 969022648 |
| -- | 1048424238 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780128012697 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0128012692 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1306737419 |
| Qualifying information | (ebk) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781306737418 |
| Qualifying information | (ebk) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 0128008822 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9780128008829 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780128008829 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)872989896 |
| Canceled/invalid control number | (OCoLC)874322618 |
| -- | (OCoLC)880316058 |
| -- | (OCoLC)880408011 |
| -- | (OCoLC)968098901 |
| -- | (OCoLC)969022648 |
| -- | (OCoLC)1048424238 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA274.25 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 003000 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 029000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 519.2 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Duan, Jinqiao, |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Effective dynamics of stochastic partial differential equations / |
| Medium | [electronic resource] |
| Statement of responsibility, etc. | Jinqiao Duan, Wei Wang. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Amsterdam : |
| Name of producer, publisher, distributor, manufacturer | Elsevier, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource. |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| Source | rda |
| 490 0# - SERIES STATEMENT | |
| Series statement | Elsevier insights |
| 500 ## - GENERAL NOTE | |
| General note | Previously issued in print: 2014. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty. Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Solutions or hints to all Exercises. |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | CIP data; resource not viewed. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Half Title; Title Page; Copyright; Dedication; Contents; Preface; 1 Introduction; 1.1 Motivation; 1.2 Examples of Stochastic Partial Differential Equations; 1.3 Outlines for This Book; 1.3.1 Chapter 2: Deterministic Partial Differential Equations; 1.3.2 Chapter 3: Stochastic Calculus in Hilbert Space; 1.3.3 Chapter 4: Stochastic Partial Differential Equations; 1.3.4 Chapter 5: Stochastic Averaging Principles; 1.3.5 Chapter 6: Slow Manifold Reduction; 1.3.6 Chapter 7: Stochastic Homogenization; 2 Deterministic Partial Differential Equations; 2.1 Fourier Series in Hilbert Space. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 2.2 Solving Linear Partial Differential Equations2.3 Integral Equalities; 2.4 Differential and Integral Inequalities; 2.5 Sobolev Inequalities; 2.6 Some Nonlinear Partial Differential Equations; 2.6.1 A Class of Parabolic PDEs; 2.6.1.1 Outline of the Proof of Theorem 2.4; 2.6.2 A Class of Hyperbolic PDEs; 2.6.2.1 Outline of the Proof of Theorem 2.5; 2.7 Problems; 3 Stochastic Calculus in Hilbert Space; 3.1 Brownian Motion and White Noise in Euclidean Space; 3.1.1 White Noise in Euclidean Space; 3.2 Deterministic Calculus in Hilbert Space; 3.3 Random Variables in Hilbert Space. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 3.4 Gaussian Random Variables in Hilbert Space3.5 Brownian Motion and White Noise in Hilbert Space; 3.5.1 White Noise in Hilbert Space; 3.6 Stochastic Calculus in Hilbert Space; 3.7 It�o's Formula in Hilbert Space; 3.8 Problems; 4 Stochastic Partial Differential Equations; 4.1 Basic Setup; 4.2 Strong and Weak Solutions; 4.3 Mild Solutions; 4.3.1 Mild Solutions of Nonautonomous spdes; 4.3.2 Mild Solutions of Autonomous spdes; 4.3.2.1 Formulation; 4.3.2.2 Well-Posedness Under Global Lipschitz Condition; 4.3.2.3 Well-Posedness Under Local Lipschitz Condition; 4.3.2.4 An Example. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.4 Martingale Solutions4.5 Conversion Between It�o and Stratonovich SPDEs; 4.5.1 Case of Scalar Multiplicative Noise; 4.5.2 Case of General Multiplicative Noise; 4.5.3 Examples; 4.6 Linear Stochastic Partial Differential Equations; 4.6.1 Wave Equation with Additive Noise; 4.6.2 Heat Equation with Multiplicative Noise; 4.7 Effects of Noise on Solution Paths; 4.7.1 Stochastic Burgers' Equation; 4.7.2 Likelihood for Remaining Bounded; 4.8 Large Deviations for SPDEs; 4.9 Infinite Dimensional Stochastic Dynamics; 4.9.1 Basic Concepts; 4.9.2 More Dynamical Systems Concepts. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.10 Random Dynamical Systems Defined by SPDEs4.10.1 Canonical Probability Space for SPDEs; 4.10.2 Perfection of Cocycles; 4.10.3 Examples; 4.11 Problems; 5 Stochastic Averaging Principles; 5.1 Classical Results on Averaging; 5.1.1 Averaging in Finite Dimension; 5.1.2 Averaging in Infinite Dimension; 5.2 An Averaging Principle for Slow-Fast SPDEs; 5.3 Proof of the Averaging Principle Theorem 5.20; 5.3.1 Some a priori Estimates; 5.3.2 Averaging as an Approximation; 5.4 A Normal Deviation Principle for Slow-Fast SPDEs; 5.5 Proof of the Normal Deviation Principle Theorem 5.34. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Stochastic partial differential equations. |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Applied. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | MATHEMATICS |
| General subdivision | Probability & Statistics |
| -- | General. |
| Source of heading or term | bisacsh |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Stochastic partial differential equations. |
| Source of heading or term | fast |
| Authority record control number | (OCoLC)fst01133516 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Wang, Wei, |
| Relator term | author. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| International Standard Book Number | 9780128008829 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Materials specified | ScienceDirect |
| Uniform Resource Identifier | http://www.sciencedirect.com/science/book/9780128008829 |
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