You can now add your name to our electronic mailing list

Carleman Estimates for Coefficient Inverse Problems and Numerical Applications

Inverse and Ill-Posed Problems Series

Michael V. Klibanov and Alexandre Timonov

This is the first book dedicated to applying the Carleman estimates to coefficient inverse problems. Coefficient inverse problems consist of determining the variable coefficients of partial differential equations from the boundary measurements of their solutions. Such problems arise in a number of applications of particular interest to natural sciences and technology, such as medical imaging, underwater acoustics and electromagnetics, non-destructive evaluation, geophysics of exploration, etc.. The main difficulty in solving coefficient inverse problems is due to their nonlinearity and ill-posedness. This monograph presents one of the most powerful tools for the mathematical treatment of such problems, the method of Carleman estimates. Originally introduced in the field of inverse problems by A.L. Bukhgeim and M.V. Klibanov in 1981, the method of Carleman estimates has become popular in the applied mathematics community. Written in a readable and concise manner, the book introduces the reader to the essence of the techniques used for deriving Carleman estimates and using them for proofs of global uniqueness and stability results for coefficient inverse problems. The core of the book is two most recent advances of the authors. These are the global uniqueness of a multidimensional coefficient inverse problem for a nonlinear parabolic equation and the so-called convexification framework for constructing globally convergent algorithms for the numerical solution of coefficient inverse problems. Several applications of the convexification to magnetotelluric frequency sounding, electrical impedance tomography, infra-red optical sensing of biotissies, and time reversal are discussed. The effectiveness of convexification algorithms is demonstrated in computational experiments.

This monograph is of value and interest to researchers in the fields of inverse problems in partial differential equations, numerical methods, mathematical modeling, scientific computing, in both academia and industry.

2004; vi pages
ISBN 90-6764-405-6
Price: EUR 150/US$ 203