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)
Resource Information
The item Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 This book is a selfcontained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by nonoverdetermining data of solutions. The formulation is different from that of DirichlettoNeumann 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.
 Language
 eng
 Extent
 1 online resource (XII, 260 pages)
 Contents

 1. Basics of Carleman estimates
 2. Basic tools of Riemannian geometry
 3. Wellposedness 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 LaplaceBeltrami operator with an extra elliptic variable and applications
 Isbn
 9784431566007
 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
 Language
 eng
 Summary
 This book is a selfcontained account of the method based on Carleman estimates for inverse problems of determining spatially varying functions of differential equations of the hyperbolic type by nonoverdetermining data of solutions. The formulation is different from that of DirichlettoNeumann 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.
 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)
 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. Wellposedness 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 LaplaceBeltrami operator with an extra elliptic variable and applications
 Control code
 9784431566007
 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, noncommercial 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
 10.1007/9784431566007
 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)
 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. Wellposedness 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 LaplaceBeltrami operator with an extra elliptic variable and applications
 Control code
 9784431566007
 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, noncommercial 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
 10.1007/9784431566007
 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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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/CarlemanEstimatesandApplicationstoInverse/Q9y6UrcKa8o/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/CarlemanEstimatesandApplicationstoInverse/Q9y6UrcKa8o/">Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems, by Mourad Bellassoued, Masahiro Yamamoto, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>