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The Resource Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (electronic resource)
Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (electronic resource)
Resource Information
The item Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (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 Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (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
 PREFACE The theory of differentialoperator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differentialoperator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTNHPRNCT200200274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. SanchezPalencia [LS]
 Language

 eng
 eng
 Extent
 1 online resource (XXII, 209 p.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1. General notions, definitions, and results
 1. Introduction
 2. General notions from functional analysis
 2.4 Dual spaces
 3. Vectorvalued functions in Banach spaces
 4. Semigroup of linear bounded operators in a Banach space
 5. Differentialoperator equations and fold completeness
 6. Isomorphism and coerciveness
 7. Interpolation of spaces
 8. Useful theorems
 2. Thermal conduction in a halfstrip and a sector
 1. Asymptotic expansion for the thermal conduction in a plate
 2. Completeness of a system of root functions for the thermal conduction in a halfstrip and a sector with smooth coefficients
 3. Completeness of a system of root functions for the thermal conduction in a halfstrip with piecewise smooth coefficients
 3. Elasticity problems in a halfstrip
 1. Asymptotic expansion for the elasticity in a plate
 2. Completeness of a system of root functions for elasticity problems in a halfstrip
 3. Thermoelasticity systems in bounded domains with nonsmooth boundaries
 4. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semiinfinite tube domains
 1. Abstract results for second order elliptic equations
 2. Boundary value problems for second order elliptic equations
 3. Boundary value problems for fourth order elliptic equations
 5. Basis property of elementary solutions for second order elliptic equations in semiinfinite tube domains
 1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient
 4. Boundary value problems for second order elliptic equations
 Problems
 References
 List of notations
 Author index
 Isbn
 9789400710801
 Label
 Application of Abstract Differential Equations to Some Mechanical Problems
 Title
 Application of Abstract Differential Equations to Some Mechanical Problems
 Statement of responsibility
 by Isabelle Titeux, Yakov Yakubov
 Language

 eng
 eng
 Summary
 PREFACE The theory of differentialoperator equations has been described in various monographs, but the initial physical problem which leads to these equations is often hidden. When the physical problem is studied, the mathematical proofs are either not given or are quickly explained. In this book, we give a systematic treatment of the partial differential equations which arise in elastostatic problems. In particular, we study problems which are obtained from asymptotic expansion with two scales. Here the methods of operator pencils and differentialoperator equations are used. This book is intended for scientists and graduate students in Functional Analy sis, Differential Equations, Equations of Mathematical Physics, and related topics. It would undoubtedly be very useful for mechanics and theoretical physicists. We would like to thank Professors S. Yakubov and S. Kamin for helpfull dis cussions of some parts of the book. The work on the book was also partially supported by the European Community Program RTNHPRNCT200200274. xiii INTRODUCTION In first two sections of the introduction, a classical mathematical problem will be exposed: the Laplace problem. The domain of definition will be, on the first time, an infinite strip and on the second time, a sector. To solve this problem, a well known separation of variables method will be used. In this way, the structure of the solution can be explicitly found. For more details about the separation of variables method exposed in this part, the reader can refer to, for example, the book by D. Leguillon and E. SanchezPalencia [LS]
 http://library.link/vocab/creatorName
 Titeux, Isabelle
 Dewey number
 515.353
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 gbvJACfZVmA
 QcPBneYqGjs
 Image bit depth
 0
 Language note
 English
 LC call number
 QA370380
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Yakubov, Yakov.
 Series statement
 Mathematics and Its Applications
 Series volume
 558
 http://library.link/vocab/subjectName

 Differential equations, partial
 Mechanics
 Mechanics, Applied
 Operator theory
 Differential Equations
 Partial Differential Equations
 Classical Mechanics
 Solid Mechanics
 Operator Theory
 Ordinary Differential Equations
 Label
 Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Incudes bibliographical references and indexes
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 1. General notions, definitions, and results  1. Introduction  2. General notions from functional analysis  2.4 Dual spaces  3. Vectorvalued functions in Banach spaces  4. Semigroup of linear bounded operators in a Banach space  5. Differentialoperator equations and fold completeness  6. Isomorphism and coerciveness  7. Interpolation of spaces  8. Useful theorems  2. Thermal conduction in a halfstrip and a sector  1. Asymptotic expansion for the thermal conduction in a plate  2. Completeness of a system of root functions for the thermal conduction in a halfstrip and a sector with smooth coefficients  3. Completeness of a system of root functions for the thermal conduction in a halfstrip with piecewise smooth coefficients  3. Elasticity problems in a halfstrip  1. Asymptotic expansion for the elasticity in a plate  2. Completeness of a system of root functions for elasticity problems in a halfstrip  3. Thermoelasticity systems in bounded domains with nonsmooth boundaries  4. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semiinfinite tube domains  1. Abstract results for second order elliptic equations  2. Boundary value problems for second order elliptic equations  3. Boundary value problems for fourth order elliptic equations  5. Basis property of elementary solutions for second order elliptic equations in semiinfinite tube domains  1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient  4. Boundary value problems for second order elliptic equations  Problems  References  List of notations  Author index
 Dimensions
 unknown
 Extent
 1 online resource (XXII, 209 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9789400710801
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9789400710801
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000115789
 (SSID)ssj0001295858
 (PQKBManifestationID)11748635
 (PQKBTitleCode)TC0001295858
 (PQKBWorkID)11347134
 (PQKB)11605261
 (DEHe213)9789400710801
 (MiAaPQ)EBC3102354
 (EXLCZ)993400000000115789
 Label
 Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Incudes bibliographical references and indexes
 Carrier category
 online resource
 Carrier category code
 cr
 Color
 not applicable
 Content category
 text
 Content type code
 txt
 Contents
 1. General notions, definitions, and results  1. Introduction  2. General notions from functional analysis  2.4 Dual spaces  3. Vectorvalued functions in Banach spaces  4. Semigroup of linear bounded operators in a Banach space  5. Differentialoperator equations and fold completeness  6. Isomorphism and coerciveness  7. Interpolation of spaces  8. Useful theorems  2. Thermal conduction in a halfstrip and a sector  1. Asymptotic expansion for the thermal conduction in a plate  2. Completeness of a system of root functions for the thermal conduction in a halfstrip and a sector with smooth coefficients  3. Completeness of a system of root functions for the thermal conduction in a halfstrip with piecewise smooth coefficients  3. Elasticity problems in a halfstrip  1. Asymptotic expansion for the elasticity in a plate  2. Completeness of a system of root functions for elasticity problems in a halfstrip  3. Thermoelasticity systems in bounded domains with nonsmooth boundaries  4. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semiinfinite tube domains  1. Abstract results for second order elliptic equations  2. Boundary value problems for second order elliptic equations  3. Boundary value problems for fourth order elliptic equations  5. Basis property of elementary solutions for second order elliptic equations in semiinfinite tube domains  1. Abstract results for second order elliptic equations with a selfadjoint operator coefficient  4. Boundary value problems for second order elliptic equations  Problems  References  List of notations  Author index
 Dimensions
 unknown
 Extent
 1 online resource (XXII, 209 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9789400710801
 Level of compression
 uncompressed
 Media category
 computer
 Media type code
 c
 Other control number
 10.1007/9789400710801
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000115789
 (SSID)ssj0001295858
 (PQKBManifestationID)11748635
 (PQKBTitleCode)TC0001295858
 (PQKBWorkID)11347134
 (PQKB)11605261
 (DEHe213)9789400710801
 (MiAaPQ)EBC3102354
 (EXLCZ)993400000000115789
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