The Resource Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)

Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)

Label
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
Title
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems
Statement of responsibility
by Mourad Bellassoued, Masahiro Yamamoto
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
This book is a self-contained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by non-overdetermining data of solutions. The formulation is different from that of Dirichlet-to-Neumann maps and can often prove the global uniqueness and Lipschitz stability even with a single measurement. These types of inverse problems include coefficient inverse problems of determining physical parameters in inhomogeneous media that appear in many applications related to electromagnetism, elasticity, and related phenomena. Although the methodology was created in 1981 by Bukhgeim and Klibanov, its comprehensive development has been accomplished only recently. In spite of the wide applicability of the method, there are few monographs focusing on combined accounts of Carleman estimates and applications to inverse problems. The aim in this book is to fill that gap. The basic tool is Carleman estimates, the theory of which has been established within a very general framework, so that the method using Carleman estimates for inverse problems is misunderstood as being very difficult. The main purpose of the book is to provide an accessible approach to the methodology. To accomplish that goal, the authors include a direct derivation of Carleman estimates, the derivation being based essentially on elementary calculus working flexibly for various equations. Because the inverse problem depends heavily on respective equations, too general and abstract an approach may not be balanced. Thus a direct and concrete means was chosen not only because it is friendly to readers but also is much more relevant. By practical necessity, there is surely a wide range of inverse problems and the method delineated here can solve them. The intention is for readers to learn that method and then apply it to solving new inverse problems
Member of
http://library.link/vocab/creatorName
Bellassoued, Mourad
Dewey number
515.353
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • FZmsBJ0AqHg
  • XeXgefhv5B8
Image bit depth
0
LC call number
QA370-380
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Yamamoto, Masahiro.
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Differential equations, partial
  • Functional analysis
  • Global differential geometry
  • Cell aggregation
  • Partial Differential Equations
  • Functional Analysis
  • Differential Geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Mathematical Physics
Label
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)
Instantiates
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Basics of Carleman estimates -- 2. Basic tools of Riemannian geometry -- 3. Well-posedness and regularity of the wave equation with variable coefficients -- 4. Carleman estimate of the wave equation in a Riemannian manifold -- 5. Inverse problem and Exact controllability for the wave equation in a Riemannian manifold -- 6. Carleman estimates for some thermoelasticity systems -- 7. Inverse heat source problem for the thermoelasticity system with variable coefficients -- 8. New realization of the pseudoconvexity -- 9. Stability in an inverse problem for a hyperbolic equation with a finite set of boundary data -- 10. Global Carleman estimate for the Laplace-Beltrami operator with an extra elliptic variable and applications
Dimensions
unknown
Edition
1st ed. 2017.
Extent
1 online resource (XII, 260 p. 7 illus., 2 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9784431566007
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-4-431-56600-7
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4340000000223617
  • (DE-He213)978-4-431-56600-7
  • (MiAaPQ)EBC5161596
  • (EXLCZ)994340000000223617
Label
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)
Publication
Antecedent source
mixed
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
not applicable
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
1. Basics of Carleman estimates -- 2. Basic tools of Riemannian geometry -- 3. Well-posedness and regularity of the wave equation with variable coefficients -- 4. Carleman estimate of the wave equation in a Riemannian manifold -- 5. Inverse problem and Exact controllability for the wave equation in a Riemannian manifold -- 6. Carleman estimates for some thermoelasticity systems -- 7. Inverse heat source problem for the thermoelasticity system with variable coefficients -- 8. New realization of the pseudoconvexity -- 9. Stability in an inverse problem for a hyperbolic equation with a finite set of boundary data -- 10. Global Carleman estimate for the Laplace-Beltrami operator with an extra elliptic variable and applications
Dimensions
unknown
Edition
1st ed. 2017.
Extent
1 online resource (XII, 260 p. 7 illus., 2 illus. in color.)
File format
multiple file formats
Form of item
online
Isbn
9784431566007
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-4-431-56600-7
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
  • (CKB)4340000000223617
  • (DE-He213)978-4-431-56600-7
  • (MiAaPQ)EBC5161596
  • (EXLCZ)994340000000223617

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