Inverse Problems for Partial Differential Equations

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Springer Science & Business Media, 29 Haz 2013 - 286 sayfa
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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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İçindekiler

IllPosed Problems and Regularization
20
Uniqueness and Stability in the Cauchy Problem
39
Single Boundary Measurements
73
Many Boundary Measurements
105
Scattering Problems
144
Integral Geometry and Tomography
163
Hyperbolic Equations
184
Parabolic Equations
218
Some Numerical Methods
247
Appendix Functional Spaces
265
Index
283
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