Geodesic
One-dimensional inverse coefficient problems of anisotropic viscoelasticity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 786-811

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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
Mots-clés : kernel. 
@article{SEMR_2019_16_a88,
     author = {Zh. D. Totieva},
     title = {One-dimensional inverse coefficient problems of anisotropic viscoelasticity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {786--811},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a88/}
}
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Zh. D. Totieva. One-dimensional inverse coefficient problems of anisotropic viscoelasticity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 786-811. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a88/