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)

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
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
PREFACE The theory of differential-operator 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 differential-operator 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 RTN-HPRN-CT-2002-00274. 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. Sanchez-Palencia [LS]
Member of
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
QA370-380
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)
Instantiates
Publication
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. Vector-valued functions in Banach spaces -- 4. Semigroup of linear bounded operators in a Banach space -- 5. Differential-operator equations and fold completeness -- 6. Isomorphism and coerciveness -- 7. Interpolation of spaces -- 8. Useful theorems -- 2. Thermal conduction in a half-strip 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 half-strip and a sector with smooth coefficients -- 3. Completeness of a system of root functions for the thermal conduction in a half-strip with piecewise smooth coefficients -- 3. Elasticity problems in a half-strip -- 1. Asymptotic expansion for the elasticity in a plate -- 2. Completeness of a system of root functions for elasticity problems in a half-strip -- 3. Thermoelasticity systems in bounded domains with non-smooth boundaries -- 4. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite 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 semi-infinite 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
10.1007/978-94-007-1080-1
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
  • (DE-He213)978-94-007-1080-1
  • (MiAaPQ)EBC3102354
  • (EXLCZ)993400000000115789
Label
Application of Abstract Differential Equations to Some Mechanical Problems, by Isabelle Titeux, Yakov Yakubov, (electronic resource)
Publication
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. Vector-valued functions in Banach spaces -- 4. Semigroup of linear bounded operators in a Banach space -- 5. Differential-operator equations and fold completeness -- 6. Isomorphism and coerciveness -- 7. Interpolation of spaces -- 8. Useful theorems -- 2. Thermal conduction in a half-strip 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 half-strip and a sector with smooth coefficients -- 3. Completeness of a system of root functions for the thermal conduction in a half-strip with piecewise smooth coefficients -- 3. Elasticity problems in a half-strip -- 1. Asymptotic expansion for the elasticity in a plate -- 2. Completeness of a system of root functions for elasticity problems in a half-strip -- 3. Thermoelasticity systems in bounded domains with non-smooth boundaries -- 4. Completeness of elementary solutions of problems for second and fourth orders elliptic equations in semi-infinite 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 semi-infinite 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
10.1007/978-94-007-1080-1
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
  • (DE-He213)978-94-007-1080-1
  • (MiAaPQ)EBC3102354
  • (EXLCZ)993400000000115789

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