-- As is known, a broad class of inverse problems for hyperbolic equations and systems reduces to the Volterra operator equations of the first or second kind with Volterra and boundedly Lipschitzcontinuous kernels [15-17]. In this work the above properties are shown to ensure the well-posedness of inverse problems locally and in the neighborhood of the exact solution as a whole. The procedure developed allows us to estimate the rate of convergence in the finite-difference scheme inversion method in solving the inverse problems for hyperbolic equations and systems. 1. POSING THE PROBLEM AND EXAMPLES The problems of determining the coefficients in hyperbolic equations and systems using some additional information on their solution are of great practical importance. The unknown coefficients, as a rule, are such important characteristics of the media being studied as Lamo parameters and density in case of an inverse problem in the theory of elasticity, the tensors of dielectric permittivity, magnetic permeability and conductivity in case of an inverse problem in electrodynamics; the velocity of wave propagation in a medium and density in case of an inverse problem in acoustics and so on. The inverse problems for hyperbolic equations belong to ill-posed problems of mathematical
Journal of Inverse and Ill-Posed Problems – de Gruyter
Published: Jan 1, 1993
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