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1. Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems.

Author

Klibanov, Michael V.

Subjects
*CARLEMAN theorem, *INVERSE problems, *MATHEMATICS, *QUASIANALYTIC functions, *STOCHASTIC convergence, *NUMERICAL analysis, *ALGORITHMS
Abstract

This is a review paper of the role of Carleman estimates in the theory of multidimensional coefficient inverse problems since the first inception of this idea in 1981. [ABSTRACT FROM AUTHOR]

Published
2013
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2. Validating the diffusion model for long-term coastal profile evolution.

Author

Avdeev, A. V., Goriounov, E. V., Lavrentiev, M. M., and Spigler, R.

Subjects
*INVERSE problems, *DIFFERENTIAL equations, *ALGORITHMS, *MATHEMATICS, *NUMERICAL analysis
Abstract

An algorithm for the simultaneous determination of two coefficients in an inverse problem for equations of the parabolic type is studied. The model under investigation has been proposed by H. de Vriend and M. Capobianco to describe the long-time coastal profile evolution. The iterative inversion procedure is based on the minimization of a suitable cost functional. Results of numerical tests are shown to illustrate the performance of the algorithm. The real measured data of the coastal profile evolution have been numerically processed to validate the aforementioned diffusion type model. The paper is targetly oriented to attract attention of professionals, who study Inverse Problems, to such new area of applications as Coastal Engineering. [ABSTRACT FROM AUTHOR]

Published
2004
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