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This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
List of contents
Introduction.- Part I: Detection of Small Conductivity Inclusions; Transmission Problem; Generalized Polarization Tensors; Derivation of the Full Asymptotic Formula; Detection of Inclusions.- Part II: Detection of Small Elastic Inclusions; Transmission Problem for Elastostatics; Elastic Moment Tensor; Derivation of Small Asymptotic Expansions; Detections of Inclusions.- Part III: Detection of Small Electromagnetic Inclusions; Well-Posedness; Representation of Solutions; Derivation of Asymptotic Formulae; Reconstruction Algorithms.- Appendices.- References.- Index.
Report
From the reviews:
"The book ... describes a 'fresh and promising techniques for the reconstruction of small inclusions from boundary measurements' and the presentation is 'intended to be self-contained'. ... The problems discussed in the book are of interest both theoretically and practically. This book hopefully will stimulate the research in the area of finding small inhomogeneities from experimental data." (Alexander G. Ramm, Zentralblatt MATH, Vol. 1113 (15), 2007)
