Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences)

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9780387253640: Inverse Problems for Partial Differential Equations (Applied Mathematical Sciences)

A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurement. By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

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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.

Review:

From the reviews of the second edition:

"The first edition of this excellent book appeared in 1998 and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. ... The second edition is considerably expanded and reflects important recent developments in the field ... . Some of the research problems from the first edition have been solved ... ." (Johannes Elschner, Zentralblatt MATH, Vol. 1092 (18), 2006)

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