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Sib. Èlektron. Mat. Izv., 2016, Volume 13, Pages 635–644 (Mi semr700)  

This article is cited in 2 scientific papers (total in 2 papers)

Differentical equations, dynamical systems and optimal control

The multidimensional problem of determining the density function for the system of viscoelasticity

Zh. D. Totievaab

a North Ossetian State University, ul. Vatutina, 46, 362025, Vladikavkaz, Russia
b Geophysical Institute of Vladikavkaz Scientific Center of the Russian Academy of Sciences, ul. Markova, 93a, 362002, Vladikavkaz, Russia

Abstract: 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, Lame's coefficients, density.

DOI: https://doi.org/10.17377/semi.2016.13.050

Full text: PDF file (169 kB)
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UDC: 517.958
MSC: 35L20,35R30,35Q99
Received January 25, 2016, published August 15, 2016

Citation: Zh. D. Totieva, “The multidimensional problem of determining the density function for the system of viscoelasticity”, Sib. Èlektron. Mat. Izv., 13 (2016), 635–644

Citation in format AMSBIB
\Bibitem{Tot16}
\by Zh.~D.~Totieva
\paper The multidimensional problem of determining the density function for the system of viscoelasticity
\jour Sib. \`Elektron. Mat. Izv.
\yr 2016
\vol 13
\pages 635--644
\mathnet{http://mi.mathnet.ru/semr700}
\crossref{https://doi.org/10.17377/semi.2016.13.050}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zh. D. Totieva, “The problem of determining the piezoelectric module of electroviscoelasticity equation”, Math. Meth. Appl. Sci., 41:16 (2018), 6409–6421  crossref  mathscinet  zmath  isi  scopus
    2. Zh. D. Totieva, “Odnomernye obratnye koeffitsientnye zadachi anizotropnoi vyazkouprugosti”, Sib. elektron. matem. izv., 16 (2019), 786–811  mathnet  crossref
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