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Inverse problem for viscoelastic system in a vertically layered medium
  • Asliddin Boltaev,
  • D. K. Durdiev
Asliddin Boltaev
Bukhara State University

Corresponding Author:[email protected]

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D. K. Durdiev
Bukhara Branch of the Institute of Mathematics at the Academy of Sciences of the Republic of Uzbekistan, Bukhara, Uzbekistan
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For the reduced canonical system of integro-differential equations of viscoelasticity, direct and inverse problems of determining the velocity field of elastic waves and the relaxation matrix are posed. The problems are replaced by a closed system of integral equations of the second kind of Volterra type with respect to the Fourier transform in the variables $x_1$, $x_2$ for solving the direct problem and unknowns of the inverse problem. Further, the method of contraction mappings in the space of continuous functions with a weighted norm is applied to this system. Thus, we prove global existence and uniqueness theorems for solutions to the problems posed.