RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Vladikavkaz. Mat. Zh.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (296 kB)
References: PDF file   HTML file
UDC: 517.958

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
\Bibitem{DurTot15} \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 \mathnet{http://mi.mathnet.ru/vmj560} 

• http://mi.mathnet.ru/eng/vmj560
• http://mi.mathnet.ru/eng/vmj/v17/i4/p18

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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
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
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
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
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
8. Zh. D. Totieva, “The problem of determining the piezoelectric module of electroviscoelasticity equation”, Math. Meth. Appl. Sci., 41:16 (2018), 6409–6421
9. Zh. Sh. Safarov, D. K. Durdiev, “Inverse problem for an integro-differential equation of acoustics”, Differ. Equ., 54:1 (2018), 134–142
•  Number of views: This page: 250 Full text: 90 References: 28