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The Resource Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource)
Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource)
Resource Information
The item Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 After over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a wellestablished discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools. A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multiscale engineering applications involving hierarchies of gridlike domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs. The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, indepth, and selfcontained study of the asymptotics of optimal control problems related to reticulated domains—the first such study in the literature. Specific topics covered in the work include: * a mostly selfcontained mathematical theory of PDEs on reticulated domains; * the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces; * convergence of optimal control problems in variable spaces; * an introduction to the asymptotic analysis of optimal control problems; * optimal control problems dealing with illposed objects on thin periodic structures, thick periodic singular graphs, thick multistructures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures. Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains
 Language

 eng
 eng
 Edition
 1st ed. 2011.
 Extent
 1 online resource (638 p.)
 Note
 Description based upon print version of record
 Contents

 Introduction
 Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools
 Background Material on Asymptotic Analysis of External Problems
 Variational Methods of Optimal Control Theory
 Suboptimal and Approximate Solutions to External Problems
 Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples
 Convergence Concepts in Variable Banach Spaces
 Convergence of Sets in Variable Spaces
 Passing to the Limit in Constrained Minimization Problems
 Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions
 Suboptimal Control of Linear SteadyStates Processes on Thin Periodic Structures with Mixed Boundary Controls
 Approximate Solutions of Optimal Control Problems for IllPosed Objects on Thin Periodic Structures
 Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures
 Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes
 Asymptotic Analysis of Elliptic Optimal Control Problems in Thick MultiStructures with Dirichlet and Neumann Boundary Controls
 Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick MultiStructures
 Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains
 Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation
 References
 Index
 Isbn
 9781283351096
 Label
 Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis
 Title
 Optimal Control Problems for Partial Differential Equations on Reticulated Domains
 Title remainder
 Approximation and Asymptotic Analysis
 Statement of responsibility
 by Peter I. Kogut, Günter R. Leugering
 Subject

 Control and Systems Theory
 Control engineering
 Engineering mathematics
 Mathematical and Computational Engineering
 Mechanics
 Mechanics, Applied
 Partial Differential Equations
 Partial differential equations
 Solid Mechanics
 System theory
 Systems Theory, Control
 Applied mathematics
 Calculus of Variations and Optimal Control; Optimization
 Calculus of variations
 Language

 eng
 eng
 Summary
 After over 50 years of increasing scientific interest, optimal control of partial differential equations (PDEs) has developed into a wellestablished discipline in mathematics with myriad applications to science and engineering. As the field has grown, so too has the complexity of the systems it describes; the numerical realization of optimal controls has become increasingly difficult, demanding ever more sophisticated mathematical tools. A comprehensive monograph on the subject, Optimal Control of Partial Differential Equations on Reticulated Domains is intended to address some of the obstacles that face researchers today, particularly with regard to multiscale engineering applications involving hierarchies of gridlike domains. Bringing original results together with others previously scattered across the literature, it tackles computational challenges by exploiting asymptotic analysis and harnessing differences between optimal control problems and their underlying PDEs. The book consists of two parts, the first of which can be viewed as a compendium of modern optimal control theory in Banach spaces. The second part is a focused, indepth, and selfcontained study of the asymptotics of optimal control problems related to reticulated domains—the first such study in the literature. Specific topics covered in the work include: * a mostly selfcontained mathematical theory of PDEs on reticulated domains; * the concept of optimal control problems for PDEs in varying such domains, and hence, in varying Banach spaces; * convergence of optimal control problems in variable spaces; * an introduction to the asymptotic analysis of optimal control problems; * optimal control problems dealing with illposed objects on thin periodic structures, thick periodic singular graphs, thick multistructures with Dirichlet and Neumann boundary controls, and coefficients on reticulated structures. Serving as both a text on abstract optimal control problems and a monograph where specific applications are explored, this book is an excellent reference for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains
 http://library.link/vocab/creatorName
 Kogut, Peter I
 Dewey number
 515.353
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 FnyMtACCN78
 AQVHKldihzY
 Language note
 English
 LC call number

 Q295
 QA402.3402.37
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Leugering, Günter R.
 Series statement
 Systems & Control: Foundations & Applications,
 http://library.link/vocab/subjectName

 System theory
 Control engineering
 Calculus of variations
 Partial differential equations
 Applied mathematics
 Engineering mathematics
 Mechanics
 Mechanics, Applied
 Systems Theory, Control
 Control and Systems Theory
 Calculus of Variations and Optimal Control; Optimization
 Partial Differential Equations
 Mathematical and Computational Engineering
 Solid Mechanics
 Label
 Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Introduction  Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools  Background Material on Asymptotic Analysis of External Problems  Variational Methods of Optimal Control Theory  Suboptimal and Approximate Solutions to External Problems  Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples  Convergence Concepts in Variable Banach Spaces  Convergence of Sets in Variable Spaces  Passing to the Limit in Constrained Minimization Problems  Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions  Suboptimal Control of Linear SteadyStates Processes on Thin Periodic Structures with Mixed Boundary Controls  Approximate Solutions of Optimal Control Problems for IllPosed Objects on Thin Periodic Structures  Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures  Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes  Asymptotic Analysis of Elliptic Optimal Control Problems in Thick MultiStructures with Dirichlet and Neumann Boundary Controls  Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick MultiStructures  Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains  Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation  References  Index
 Dimensions
 unknown
 Edition
 1st ed. 2011.
 Extent
 1 online resource (638 p.)
 Form of item
 online
 Isbn
 9781283351096
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780817681494
 Specific material designation
 remote
 System control number

 (CKB)2550000000046044
 (EBL)798957
 (OCoLC)747105258
 (SSID)ssj0000610481
 (PQKBManifestationID)11428340
 (PQKBTitleCode)TC0000610481
 (PQKBWorkID)10638481
 (PQKB)10655431
 (DEHe213)9780817681494
 (MiAaPQ)EBC798957
 (EXLCZ)992550000000046044
 Label
 Optimal Control Problems for Partial Differential Equations on Reticulated Domains : Approximation and Asymptotic Analysis, by Peter I. Kogut, Günter R. Leugering, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Introduction  Part I. Asymptotic Analysis of Optimal Control Problems for Partial Differential Equations: Basic Tools  Background Material on Asymptotic Analysis of External Problems  Variational Methods of Optimal Control Theory  Suboptimal and Approximate Solutions to External Problems  Introduction to the Asymptotic Analysis of Optimal Control Problems: A Parade of Examples  Convergence Concepts in Variable Banach Spaces  Convergence of Sets in Variable Spaces  Passing to the Limit in Constrained Minimization Problems  Part II. Optimal Control Problems on Periodic Reticulated Domains: Asymptotic Analysis and Approximate Solutions  Suboptimal Control of Linear SteadyStates Processes on Thin Periodic Structures with Mixed Boundary Controls  Approximate Solutions of Optimal Control Problems for IllPosed Objects on Thin Periodic Structures  Asymptotic Analysis of Optimal Control Problems on Periodic Singular Structures  Suboptimal Boundary Control of Elliptic Equations in Domains with Small Holes  Asymptotic Analysis of Elliptic Optimal Control Problems in Thick MultiStructures with Dirichlet and Neumann Boundary Controls  Gap Phenomenon in Modeling of Suboptimal Controls to Parabolic Optimal Control Problems in Thick MultiStructures  Boundary Velocity Suboptimal Control of Incompressible Flow in Cylindrically Perforated Domains  Optimal Control Problems in Coefficients: Sensitivity Analysis and Approximation  References  Index
 Dimensions
 unknown
 Edition
 1st ed. 2011.
 Extent
 1 online resource (638 p.)
 Form of item
 online
 Isbn
 9781283351096
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780817681494
 Specific material designation
 remote
 System control number

 (CKB)2550000000046044
 (EBL)798957
 (OCoLC)747105258
 (SSID)ssj0000610481
 (PQKBManifestationID)11428340
 (PQKBTitleCode)TC0000610481
 (PQKBWorkID)10638481
 (PQKB)10655431
 (DEHe213)9780817681494
 (MiAaPQ)EBC798957
 (EXLCZ)992550000000046044
Subject
 Control and Systems Theory
 Control engineering
 Engineering mathematics
 Mathematical and Computational Engineering
 Mechanics
 Mechanics, Applied
 Partial Differential Equations
 Partial differential equations
 Solid Mechanics
 System theory
 Systems Theory, Control
 Applied mathematics
 Calculus of Variations and Optimal Control; Optimization
 Calculus of variations
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