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DOI: 10.23671/VNC.2015.4.5969

The problem of determining the multidimensional kernel of viscoelasticity equation

Totieva, Zh. D. ,  Durdiev D. Q.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 4.
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 \(t\).
Keywords: inverse problem, stability, delta function, Lame's coefficients, kernel
Language: Russian Download the full text  
For citation: Totieva Zh. D., Durdiev D. Q. The problem of determining the multidimensional kernel of viscoelasticity equation. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 4, pp.18-43. DOI 10.23671/VNC.2015.4.5969
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