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Applications of Elliptic Carleman Inequalities to Cauchy and Inverse Problems / by Mourad Choulli.
Springer Nature - Springer Mathematics and Statistics eBooks 2016 English International Available online
View online- Format:
- Book
- Author/Creator:
- Choulli, Mourad, Author.
- Series:
- SpringerBriefs in Mathematics, 2191-8201
- Language:
- English
- Subjects (All):
- Differential equations.
- Mathematical physics.
- Cancer.
- Mathematics.
- Engineering mathematics.
- Engineering--Data processing.
- Engineering.
- Differential Equations.
- Mathematical Methods in Physics.
- Cancer Biology.
- Applications of Mathematics.
- Mathematical and Computational Engineering Applications.
- Local Subjects:
- Differential Equations.
- Mathematical Methods in Physics.
- Cancer Biology.
- Applications of Mathematics.
- Mathematical and Computational Engineering Applications.
- Physical Description:
- 1 online resource (IX, 81 p.)
- Edition:
- 1st ed. 2016.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2016.
- Summary:
- This book presents a unified approach to studying the stability of both elliptic Cauchy problems and selected inverse problems. Based on elementary Carleman inequalities, it establishes three-ball inequalities, which are the key to deriving logarithmic stability estimates for elliptic Cauchy problems and are also useful in proving stability estimates for certain elliptic inverse problems. The book presents three inverse problems, the first of which consists in determining the surface impedance of an obstacle from the far field pattern. The second problem investigates the detection of corrosion by electric measurement, while the third concerns the determination of an attenuation coefficient from internal data, which is motivated by a problem encountered in biomedical imaging.
- Contents:
- 1 Preliminaries
- 2 Uniqueness of continuation and Cauchy problems
- 3 Determining the surface impedance of an obstacle from the scattering amplitude
- 4 Determining a corrosion coecient from a boundary measurement and an attenuation coecient from an internal measurement.
- Notes:
- Includes bibliographical references and index.
- ISBN:
- 3-319-33642-8
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