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June 1, 2004
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We establish the uniqueness and conditional stability in determining a heat source term from boundary measurements which are started after some time. The key is analyticity of solutions in the time and we apply the maximum principle for analytic functions.
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June 1, 2004
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In this article we study the fan-beam Radon transform of symmetrical solenoidal 2D tensor fields of arbitrary rank m in a unit disc as the operator, acting from the object space L 2 (; S m ) to the data space L 2 ([0, 2π) × [0, 2π)). The orthogonal polynomial basis of solenoidal tensor fields on the disc was built with the help of Zernike polynomials and then a singular value decomposition (SVD) for the operator was obtained. The inversion formula for the fan-beam tensor transform follows from this decomposition. Thus obtained inversion formula can be used as a tomographic filter for splitting a known tensor field into potential and solenoidal parts. Numerical results are presented.
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In this paper we consider a new method of constructing regularizing operators of the inverse Laplace transform. The regularizing operators constructed in this work are defined for any image function analytic for Re p > 0. The analytical dependence between exact and regularized solutions allows to analyze the rate of convergence of the regularized solution to the exact one. This analysis is illustrated by graphs and reveals the main features of the numerical inversion of the Laplace transform. The numerical examples illustrating the advantages of the proposed method in stability and accuracy are given.
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In this paper we determine, under a suitable additional information and in a framework of Gevrey (or analytic) functions with respect to a specific group of spatial variables, a coefficient q in a linear hyperbolic equation of the form (1.1) related to a spatial domain of the form Ω × × , where Ω is a (possibly non-smooth) domain in . In our context determining q means to show existence, uniqueness and continuous dependence of q on the data.