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Effective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations
  • Author : Jinqiao Duan
  • Publsiher : Elsevier
  • Release : 06 March 2014
  • ISBN : 0128012692
  • Pages : 282 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKEffective Dynamics of Stochastic Partial Differential Equations

Summary:
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


Effective Dynamics of Stochastic Partial Differential Equations

Effective Dynamics of Stochastic Partial Differential Equations
  • Author : Jinqiao Duan,Wei WANG
  • Publisher : Elsevier
  • Release : 06 March 2014
GET THIS BOOKEffective Dynamics of Stochastic Partial Differential Equations

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

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Numerical Methods for Stochastic Partial Differential Equations with White Noise

Numerical Methods for Stochastic Partial Differential Equations with White Noise
  • Author : Zhongqiang Zhang,George Em Karniadakis
  • Publisher : Springer
  • Release : 01 September 2017
GET THIS BOOKNumerical Methods for Stochastic Partial Differential Equations with White Noise

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven

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Stochastic Pdes And Modelling Of Multiscale Complex System

Stochastic Pdes And Modelling Of Multiscale Complex System
  • Author : Wang Wei,Chen Xiaopeng,Lv Yan
  • Publisher : World Scientific
  • Release : 07 May 2019
GET THIS BOOKStochastic Pdes And Modelling Of Multiscale Complex System

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the

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Approximation of Stochastic Invariant Manifolds

Approximation of Stochastic Invariant Manifolds
  • Author : Mickaël D. Chekroun,Honghu Liu,Shouhong Wang
  • Publisher : Springer
  • Release : 20 December 2014
GET THIS BOOKApproximation of Stochastic Invariant Manifolds

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

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Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations
  • Author : Mickaël D. Chekroun,Honghu Liu,Shouhong Wang
  • Publisher : Springer
  • Release : 23 December 2014
GET THIS BOOKStochastic Parameterizing Manifolds and Non-Markovian Reduced Equations

In this second volume, a general approach is developed to provide approximate parameterizations of the "small" scales by the "large" ones for a broad class of stochastic partial differential equations (SPDEs). This is accomplished via the concept of parameterizing manifolds (PMs), which are stochastic manifolds that improve, for a given realization of the noise, in mean square error the partial knowledge of the full SPDE solution when compared to its projection onto some resolved modes. Backward-forward systems are designed to

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Stochastic Ordinary and Stochastic Partial Differential Equations

Stochastic Ordinary and Stochastic Partial Differential Equations
  • Author : Peter Kotelenez
  • Publisher : Springer Science & Business Media
  • Release : 05 December 2007
GET THIS BOOKStochastic Ordinary and Stochastic Partial Differential Equations

Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.

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Shape Optimization, Homogenization and Optimal Control

Shape Optimization, Homogenization and Optimal Control
  • Author : Volker Schulz,Diaraf Seck
  • Publisher : Springer
  • Release : 05 September 2018
GET THIS BOOKShape Optimization, Homogenization and Optimal Control

The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers.

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New Trends in Stochastic Analysis and Related Topics

New Trends in Stochastic Analysis and Related Topics
  • Author : Huaizhong Zhao,Aubrey Truman
  • Publisher : World Scientific
  • Release : 19 May 2022
GET THIS BOOKNew Trends in Stochastic Analysis and Related Topics

The volume is dedicated to Professor David Elworthy to celebrate his fundamental contribution and exceptional influence on stochastic analysis and related fields. Stochastic analysis has been profoundly developed as a vital fundamental research area in mathematics in recent decades. It has been discovered to have intrinsic connections with many other areas of mathematics such as partial differential equations, functional analysis, topology, differential geometry, dynamical systems, etc. Mathematicians developed many mathematical tools in stochastic analysis to understand and model random phenomena

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Multiple Time Scale Dynamics

Multiple Time Scale Dynamics
  • Author : Christian Kuehn
  • Publisher : Springer
  • Release : 25 February 2015
GET THIS BOOKMultiple Time Scale Dynamics

This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book

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Stochastic Partial Differential Equations and Related Fields

Stochastic Partial Differential Equations and Related Fields
  • Author : Andreas Eberle,Martin Grothaus,Walter Hoh,Moritz Kassmann,Wilhelm Stannat,Gerald Trutnau
  • Publisher : Springer
  • Release : 03 July 2018
GET THIS BOOKStochastic Partial Differential Equations and Related Fields

This Festschrift contains five research surveys and thirty-four shorter contributions by participants of the conference ''Stochastic Partial Differential Equations and Related Fields'' hosted by the Faculty of Mathematics at Bielefeld University, October 10–14, 2016. The conference, attended by more than 140 participants, including PostDocs and PhD students, was held both to honor Michael Röckner's contributions to the field on the occasion of his 60th birthday and to bring together leading scientists and young researchers to present the current state of the art

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Multiscale Methods

Multiscale Methods
  • Author : Grigoris Pavliotis,Andrew Stuart
  • Publisher : Springer Science & Business Media
  • Release : 18 January 2008
GET THIS BOOKMultiscale Methods

This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well

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A Minicourse on Stochastic Partial Differential Equations

A Minicourse on Stochastic Partial Differential Equations
  • Author : Robert C. Dalang,Carl Mueller,Yimin Xiao,David Nualart
  • Publisher : Springer Science & Business Media
  • Release : 19 May 2022
GET THIS BOOKA Minicourse on Stochastic Partial Differential Equations

This title contains lectures that offer an introduction to modern topics in stochastic partial differential equations and bring together experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic PDEs.

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Extreme Man-Made and Natural Hazards in Dynamics of Structures

Extreme Man-Made and Natural Hazards in Dynamics of Structures
  • Author : Adnan Ibrahimbegovic,Ivica Kozar
  • Publisher : Springer Science & Business Media
  • Release : 16 May 2007
GET THIS BOOKExtreme Man-Made and Natural Hazards in Dynamics of Structures

This book provides a critical assessment of current knowledge and indicates new challenges which are brought about at present times by fighting man-made and natural hazards in transient analysis of structures. The latter concerns both permanently fixed structures, such as those built to protect people and/or sensitive storage material; or special structures, like bridges and tunnels; and moving structures such as trains, planes, ships or cars.

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