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Vladikavkaz. Mat. Zh., 2015, Volume 17, Number 4, Pages 18–43 (Mi vmj560)  

This article is cited in 9 scientific papers (total in 9 papers)

The problem of determining the multidimensional kernel of viscoelasticity equation

D. Q. Durdieva, Zh. D. Totievabc

a Bukhara State University, Bukhara, Uzbekistan
b Center of Geophysical Investigations of Vladikavkaz Scientific Center of the Russian Academy of Sciences and the Government of Republic of North Ossetia-Alania, Vladikavkaz, Russia
c North Ossetian State University after Kosta Levanovich Khetagurov, Vladikavkaz, Russia

Abstract: The integro-differential system of viscoelasticity equations is considered. The direct problem of determining of the displacements vector from the initial-boundary problem for this system is formulated. It is assumed that the kernel in the integral part depends on both the time and the space variable $x_2$. For its determination an additional condition relative to the first component of the displacements vector with $x_3=0$ is posed. The inverse problem is replaced by the equivalent system of integral equations. The study is based on the method of scales of Banach spaces of analytic functions. The theorem on local unique solvability of the inverse problem is proved in the class of functions analytic on the variable $x_2$ and continuous on $t$.

Key words: inverse problem, stability, delta function, Lame's coefficients, kernel.

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UDC: 517.958
Received: 09.02.2015

Citation: D. Q. Durdiev, Zh. D. Totieva, “The problem of determining the multidimensional kernel of viscoelasticity equation”, Vladikavkaz. Mat. Zh., 17:4 (2015), 18–43

Citation in format AMSBIB
\by D.~Q.~Durdiev, Zh.~D.~Totieva
\paper The problem of determining the multidimensional kernel of viscoelasticity equation
\jour Vladikavkaz. Mat. Zh.
\yr 2015
\vol 17
\issue 4
\pages 18--43

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    This publication is cited in the following articles:
    1. Zh. D. Totieva, “Mnogomernaya zadacha ob opredelenii funktsii plotnosti dlya sistemy uravnenii vyazkouprugosti”, Sib. elektron. matem. izv., 13 (2016), 635–644  mathnet  crossref
    2. D. K. Durdiev, U. D. Durdiev, “The problem of kernel determination from viscoelasticity system integro-differential equations for homogeneous anisotropic media”, Nanosyst.-Phys. Chem. Math., 7:3 (2016), 405–409  crossref  zmath  isi
    3. D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional kernel of the electroviscoelasticity equation”, Siberian Math. J., 58:3 (2017), 427–444  mathnet  crossref  crossref  isi  elib  elib
    4. Zh. D. Totieva, D. K. Durdiev, “The Problem of Finding the One-Dimensional Kernel of the Thermoviscoelasticity Equation”, Math. Notes, 103:1 (2018), 118–132  mathnet  crossref  crossref  isi  elib
    5. D. K. Durdiev, A. A. Rakhmonov, “Inverse problem for a system of integro-differential equations for SH waves in a visco-elastic porous medium: Global solvability”, Theoret. and Math. Phys., 195:3 (2018), 923–937  mathnet  crossref  crossref  adsnasa  isi  elib
    6. Zh. Sh. Safarov, “Global solvability of the one-dimensional inverse problem for the integro-differential equation of acoustics”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 753–763  mathnet  crossref
    7. D. K. Durdiev, Zh. D. Totieva, “The problem of determining the one-dimensional matrix kernel of the system of viscoelasticity equations”, Math. Meth. Appl. Sci., 41:17 (2018), 8019–8032  crossref  mathscinet  zmath  isi
    8. 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
    9. Zh. Sh. Safarov, D. K. Durdiev, “Inverse problem for an integro-differential equation of acoustics”, Differ. Equ., 54:1 (2018), 134–142  crossref  mathscinet  zmath  isi  scopus
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