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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
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
Assigning source
Provided by publisher
http://library.link/vocab/creatorName
Bellassoued, Mourad
Image bit depth
0
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Yamamoto, Masahiro.
Series statement
  • Springer eBooks
  • Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Functional analysis
  • Partial differential equations
  • Differential geometry
  • Manifolds (Mathematics)
  • Complex manifolds
  • Mathematical physics
Label
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-4-431-56600-7
Instantiates
Publication
Antecedent source
mixed
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
Control code
978-4-431-56600-7
Dimensions
unknown
Extent
1 online resource (XII, 260 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
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
Other physical details
7 illustrations, 2 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1013825366
Label
Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-4-431-56600-7
Publication
Antecedent source
mixed
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
Control code
978-4-431-56600-7
Dimensions
unknown
Extent
1 online resource (XII, 260 pages)
File format
multiple file formats
Form of item
  • online
  • electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
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
Other physical details
7 illustrations, 2 illustrations in color.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1013825366

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