Inverse problems for partial differential equations
type: Item
instance of: scholarly article
title: Inverse problems for partial differential equations
zbMATH Open document ID: 1092.35001
author: Victor Isakov
published in: Applied Mathematical Sciences
publication date: 2006-03-15T00:00:00Z
review text: The first edition of this excellent book appeared in 1998 (see Zbl 0908.35134) see and became a standard reference for everyone interested in analysis and numerics of inverse problems in partial differential equations. The topic is of substantial and growing interest for mathematicians, physicists and engineers, and to graduate students in these areas as well. The book consists of the following Chapters: 1) Inverse problems, 2) Ill-posed problems and regularization, 3) Uniqueness and stability in the Cauchy problem, 4) Elliptic equations: single boundary measurements, 5) Elliptic equations: many boundary measurements, 6) Scattering problems, 7) Integral geometry and tomography, 8) Hyperbolic equations, 9) Inverse parabolic problems, 10) Some numerical methods. The second edition is considerably expanded and reflects important recent developments in the field, including new uniqueness and stability results for basic inverse problems, emerging financial applications, and new efficient reconstruction algorithms. Some of the research problems from the first edition have been solved, while most of them still await solutions.
reviewed by: Johannes Elschner
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 35K30
Mathematics Subject Classification ID: 35P25
zbMATH DE Number: 5012646
zbMATH Keywords: inverse problem of gravimetry
zbMATH Keywords: inverse conductivity problem
zbMATH Keywords: inverse scattering problems
zbMATH Keywords: tomography
zbMATH Keywords: inverse seismic problem
zbMATH Keywords: inverse spectral problems
zbMATH Keywords: regularization
zbMATH Keywords: inverse problems of elliptic equations
zbMATH Keywords: Dirichlet-to-Neumann map
zbMATH Keywords: inverse parabolic problems
zbMATH Keywords: numerical methods
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5012646