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Article
Convexification Numerical Method for the Retrospective Problem of Mean Field Games
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the ret...
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Article
A Coefficient Inverse Problem for the Mean Field Games System
A coefficient inverse problem (CIP) of the determination of a coefficient of the mean field games system (MFGS) of the second order is considered. The input data are generated by a single measurement event. La...
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Chapter and Conference Paper
Methods of Quantitative Reconstruction of Shapes and Refractive Indices from Experimental data
In this chapter we summarize results of [5, 6, 14] and present new results of reconstruction of refractive indices and shapes of objects placed in the air from blind backscattered experimental data using two-s...
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Chapter and Conference Paper
Approximate Global Convergence in Imaging of Land Mines from Backscattered Data
We present new model of an approximate globally convergent method in the most challenging case of the backscattered data. In this case data for the coefficient inverse problem are given only at the backscatter...
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Chapter and Conference Paper
Adaptive FEM with Relaxation for a Hyperbolic Coefficient Inverse Problem
Recent research of publications (Beilina and Johnson, Numerical Mathematics and Advanced Applications: ENUMATH 2001, Springer, Berlin, 2001; Beilina, Applied and Computational Mathematics 1, 158–174, 2002; Beilin...
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Chapter
Carleman Estimates and Inverse Problems in the Last Two Decades
Carleman estimates are a powerful tool which was originally proposed by T. Carleman in 1939 for proofs of uniqueness results for ill-posed Cauchy problems. Since 1981 this tool has been applied to inverse prob...
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Chapter
Image Reconstruction from Experimental Data in Diffusion Tomography
The authors have recently introduced a novel imaging algorithm for optical/diffusion tomography, the “Elliptic Systems Method” (ESM). In this article the performance of the ESM is analyzed for experimental dat...
