Geodesic
The multidimensional problem of determining the density function for the system of viscoelasticity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 635-644

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The integro-differential system of viscoelasticity equations is considered. The problem of determining the function of density $\rho(x_2,x_3)$ is investigated. For its determination an additional condition relative to the Fourier transform of the first component of the displacements vector for $x_3 = 0$ is given. The theorems of the local unique solvability of the inverse problem is proved in the special class of functions. The stability estimate of solving the inverse problem is obtained.
Keywords: inverse problem, stability, delta function, density.
Mots-clés : Lame's coefficients 
@article{SEMR_2016_13_a78,
     author = {Zh. D. Totieva},
     title = {The multidimensional problem of determining the density function for the system of viscoelasticity},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {635--644},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a78/}
}
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Zh. D. Totieva. The multidimensional problem of determining the density function for the system of viscoelasticity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 635-644. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a78/