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Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 786–811 (Mi semr1095)  

Differentical equations, dynamical systems and optimal control

One-dimensional inverse coefficient problems of anisotropic viscoelasticity

Zh. D. Totievaab

a North Ossetian State University, 46, Vatutina str., Vladikavkaz, 362025, Russia
b Southern Mathematical Institute of Vladikavkaz Scientific Centre of Russian Academy of Sciences, 93a, Markova str., Vladikavkaz, 362002, Russia

Abstract: We consider the problem of finding the moduli of elasticity $c_{11}(x_3), c_{12}(x_3), c_{44}(x_3)$, $x_3>0$, occurring in the system of integro-differential viscoelasticity equations for gomogenious anisotropic medium. The density of medium is contant. The matrix kernel $k(t)=diag(k_1,$ $k_2,$ $k_3)(t),$ $t\in [0,T]$ is known. As additional information is the Fourier transform of the first and third component of the displacements vector for $x_3 = 0$. The results are the theorems on the existence of a unique solution of the inverse problems and the theorems of stability.

Keywords: inverse problem, stability, moduli of elasticity, delta function, kernel.

DOI: https://doi.org/10.33048/semi.2019.16.053

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Bibliographic databases:

UDC: 517.958
MSC: 35L20,35R30,35Q99
Received November 25, 2018, published June 11, 2019

Citation: Zh. D. Totieva, “One-dimensional inverse coefficient problems of anisotropic viscoelasticity”, Sib. Èlektron. Mat. Izv., 16 (2019), 786–811

Citation in format AMSBIB
\Bibitem{Tot19}
\by Zh.~D.~Totieva
\paper One-dimensional inverse coefficient problems of anisotropic viscoelasticity
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 786--811
\mathnet{http://mi.mathnet.ru/semr1095}
\crossref{https://doi.org/10.33048/semi.2019.16.053}


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