Inverse Problems for Partial Differential Equations

Victor Isakov (auth.)9780387253640, 0387253645

The topic of the inverse problems is of substantial and rapidly growing interest for many scientists and engineers. The second edition covers most important recent developments in the field of inverse problems, describing theoretical and computational methods, and emphasizing new ideas and techniques. It also reflects new changes since the first edition, including some corrections. This edition is considerably expanded, with some concepts such as pseudo-convexity, and proofs simplified. New material is added to reflect recent progress in theory of inverse problems.

This book is intended for mathematicians working with partial differential equations and their applications, and physicists, geophysicists and engineers involved with experiments in nondestructive evaluation, seismic exploration, remote sensing and tomography.

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Table of contents :
Front Matter….Pages i-xi
Inverse Problems….Pages 1-19
Ill-Posed Problems and Regularization….Pages 20-38
Uniqueness and Stability in the Cauchy Problem….Pages 39-72
Elliptic Equations. Single Boundary Measurements….Pages 73-104
Elliptic Equations: Many Boundary Measurements….Pages 105-143
Scattering problems….Pages 144-162
Integral Geometry and Tomography….Pages 163-183
Hyperbolic Problems….Pages 184-217
Inverse parabolic problems….Pages 218-246
Some Numerical Methods….Pages 247-264
Back Matter….Pages 265-286