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Russia; Uzbekistan Bukhara; Tashkent; village of Mikhailovskoye
Year
2023
Volume
33
Issue
4
Pages
581–600
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Section Mathematics
Title Inverse problem for the system of viscoelasticity in anisotropic media with tetragonal form of elasticity modulus
Author(-s) Durdiev D.K.ab, Bozorov Z.R.ab, Boltaev A.A.abc
Affiliations Bukhara State Universitya, Institute of Mathematics, National Academy of Sciences of Uzbekistanb, Vladikavkaz Scientific Center, Russian Academy of Sciencesc
Abstract 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 considered. The problems are replaced by a closed system of Volterra integral equations of the second kind with respect to the Fourier transform in the variables $x_{1}$ and $x_{2}$ for the solution of 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 of the problems.
Keywords viscoelasticity, resolvent, inverse problem, hyperbolic system, Fourier transform
UDC 517.968
MSC 35F61, 35L50, 42A38
DOI 10.35634/vm230404
Received 15 March 2023
Language English
Citation Durdiev D.K., Bozorov Z.R., Boltaev A.A. Inverse problem for the system of viscoelasticity in anisotropic media with tetragonal form of elasticity modulus, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 4, pp. 581–600.
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