
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
VSP International Science Publishers
1st Edition
Published on 31. March 2004
Book
Hardback
280 pages
978-90-6764-405-1 (ISBN)
Article exhausted; check different version
Description
This is the first book dedicated to applying the Carleman estimates to coefficient inverse problems. Written in a readable and concise manner, the book introduces the reader to the essence of the method of Carleman estimates, which is one of the most powerful tools for the mathematical treatment of coefficient inverse problems. The core of the book is two most recent advances of the authors. These are the global uniqueness of a multidimensional coefficient inverse problem for a nonlinear parabolic equation and the so-called convexification framework for constructing globally convergent algorithms for a broad class of inverse problems. Several applications of the convexification to magnetotelluric frequency sounding, electrical impedance tomography, infra-red optical sensing of biotissies, and time reversal are considered.
More details
Series
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
Professional and scholarly
US School Grade: College Graduate Student
Product notice
Laminated cover
Weight
595 gr
ISBN-13
978-90-6764-405-1 (9789067644051)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Michael V. Klibanov | Alexander A. Timonov
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
Book
approx. 01/2200
1st Edition
De Gruyter
€109.95
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Michael V. Klibanov | Alexander A. Timonov
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
E-Book
04/2012
1st Edition
De Gruyter
€260.00
Available for download

Michael V. Klibanov | Alexander A. Timonov
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
Book
01/2004
1st Edition
De Gruyter
€339.00
Article exhausted; check different version
Persons
Michael V. Klibanov,University of North Carolina, Charlotte, USA; Alexander A. Timonov, University of North Carolina, Upstate, USA.
Content
Chapter 1Introduction
1.1. Some historical remarks
1.2. Mathematical background
1.3. The concept of overdetermination
1.4. Uniqueness results in one dimension
1.5. Uniqueness results in high dimensions
1.6. A brief overview of uniqueness results
Chapter 2. Carleman estimates and ill-posed Cauchy problems
2.1. A second order partial differential operator 2.2. Examples of Carleman estimates
2.3. Uniqueness and the Holder stability
2.4. The Lipschitz stability for a hyperbolic Cauchy problem
2.5. Error estimates in the method of quasireversibility
Chapter 3. Global uniqueness results in high dimensions
3.1. Estimating a Volterra-like operator
3.2. An inverse problem for a hyperbolic equation
3.3. Some inverse problems for a parabolic equation
3.4. Inverse problems for a elliptic equation
3.5. The global uniqueness in a 2D inverse conductivity problem
Chapter 4. The global uniqueness of a nonlinear parabolic problem
4.1. Problem formulation
4.2. Statement of the main result
4.3. An estimate of an integral
4.4. The integro-differential inequality
4.5. Domains
4.6. Notations
4.7. A Carleman estimate
4.8. Proof of the main result
Chapter 5. On the numerical solution of coefficient inverse problems
5.1. Some traditional methods
5.2. Using the Dirichlet-to-Neumann map
5.3. Convexification
5.4. Strict convexity of J_{\lambda, \kappa}(q)
Chapter 6. Some globally convergent convexification algorithms
6.1. Model problems in one dimension
6.2. The recurrence minimization method
6.3. Two numerical methods for nonlinear convex programming
6.4. Error estimates
6.5. Unifying framework
Chapter 7. Some applied problems
7.1. Magnetotelluric sounding of layered media 7.2. Magnetotelluric sounding of 2D inhomogeneous media
7.3. Space electric sounding of 2D inhomogeneous media
7.4. Near-infrared optical sensing of layered biotissues
7.5. Computational time reversal
Bibliography
1.1. Some historical remarks
1.2. Mathematical background
1.3. The concept of overdetermination
1.4. Uniqueness results in one dimension
1.5. Uniqueness results in high dimensions
1.6. A brief overview of uniqueness results
Chapter 2. Carleman estimates and ill-posed Cauchy problems
2.1. A second order partial differential operator 2.2. Examples of Carleman estimates
2.3. Uniqueness and the Holder stability
2.4. The Lipschitz stability for a hyperbolic Cauchy problem
2.5. Error estimates in the method of quasireversibility
Chapter 3. Global uniqueness results in high dimensions
3.1. Estimating a Volterra-like operator
3.2. An inverse problem for a hyperbolic equation
3.3. Some inverse problems for a parabolic equation
3.4. Inverse problems for a elliptic equation
3.5. The global uniqueness in a 2D inverse conductivity problem
Chapter 4. The global uniqueness of a nonlinear parabolic problem
4.1. Problem formulation
4.2. Statement of the main result
4.3. An estimate of an integral
4.4. The integro-differential inequality
4.5. Domains
4.6. Notations
4.7. A Carleman estimate
4.8. Proof of the main result
Chapter 5. On the numerical solution of coefficient inverse problems
5.1. Some traditional methods
5.2. Using the Dirichlet-to-Neumann map
5.3. Convexification
5.4. Strict convexity of J_{\lambda, \kappa}(q)
Chapter 6. Some globally convergent convexification algorithms
6.1. Model problems in one dimension
6.2. The recurrence minimization method
6.3. Two numerical methods for nonlinear convex programming
6.4. Error estimates
6.5. Unifying framework
Chapter 7. Some applied problems
7.1. Magnetotelluric sounding of layered media 7.2. Magnetotelluric sounding of 2D inhomogeneous media
7.3. Space electric sounding of 2D inhomogeneous media
7.4. Near-infrared optical sensing of layered biotissues
7.5. Computational time reversal
Bibliography