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Inverse Problems for Partial Differential Equations

Author: Victor Isakov
Publisher: New York, NY : Springer New York : Imprint : Springer, 1998.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), 127.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub­ stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Victor Isakov
ISBN: 1489900306 9781489900302 9781489900326 1489900322 0387982566 9780387982564
OCLC Number: 1058267156
Language Note: English.
Description: 1 online resource (XI, 286 pages 1 illustration)
Contents: 1 Inverse Problems --
2 Ill-Posed Problems and Regularization --
3 Uniqueness and Stability in the Cauchy Problem --
4 Elliptic Equations: Single Boundary Measurements --
5 Elliptic Equations: Many Boundary Measurements --
6 Scattering Problems --
7 Integral Geometry and Tomography --
8 Hyperbolic Equations --
9 Parabolic Equations --
10 Some Numerical Methods --
Appendix. Functional Spaces --
References.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), 127.
Responsibility: by Victor Isakov.

Abstract:

This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub­ stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica­ tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com­ plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.

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The topic is of sub\u00AD stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica\u00AD tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com\u00AD plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.<\/span>\"@en<\/a> ;\u00A0\u00A0\u00A0\nschema:description<\/a> \"1 Inverse Problems -- 2 Ill-Posed Problems and Regularization -- 3 Uniqueness and Stability in the Cauchy Problem -- 4 Elliptic Equations: Single Boundary Measurements -- 5 Elliptic Equations: Many Boundary Measurements -- 6 Scattering Problems -- 7 Integral Geometry and Tomography -- 8 Hyperbolic Equations -- 9 Parabolic Equations -- 10 Some Numerical Methods -- Appendix. 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