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Inverse and Ill-Posed Problems Series
Michael V. Klibanov and Alexandre Timonov
This is the first book dedicated to applying the Carleman estimates tocoefficient inverse problems. Coefficient inverse problems consist ofdetermining the variable coefficients of partial differential equationsfrom the boundary measurements of their solutions. Such problems arisein a number of applications of particular interest to natural sciencesand technology, such as medical imaging, underwater acoustics andelectromagnetics, non-destructive evaluation, geophysics of exploration,etc.. The main difficulty in solving coefficient inverse problems is dueto their nonlinearity and ill-posedness. This monograph presents one ofthe most powerful tools for the mathematical treatment of such problems,the method of Carleman estimates. Originally introduced in the field ofinverse problems by A.L. Bukhgeim and M.V. Klibanov in 1981, the methodof Carleman estimates has become popular in the applied mathematicscommunity. Written in a readable and concise manner, the book introducesthe reader to the essence of the techniques used for deriving Carlemanestimates and using them for proofs of global uniqueness and stabilityresults for coefficient inverse problems. The core of the book is twomost recent advances of the authors. These are the global uniqueness ofa multidimensional coefficient inverse problem for a nonlinear parabolicequation and the so-called convexification framework for constructingglobally convergent algorithms for the numerical solution of coefficientinverse problems. Several applications of the convexification tomagnetotelluric frequency sounding, electrical impedance tomography,infra-red optical sensing of biotissies, and time reversal arediscussed. The effectiveness of convexification algorithms isdemonstrated in computational experiments.
This monograph is of value and interest to researchers in the fields ofinverse problems in partial differential equations, numerical methods,mathematical modeling, scientific computing, in both academia andindustry.
2004; vi+280 pages
Price (all prices are subject to change without notice): EUR 159/US$ 227