NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2016, 7 (3), P. 405–409
The problem of kernel determination from viscoelasticity system integro-differential equations for homogeneous anisotropic media
D. K. Durdiev – Bukhara State University, Bukhara, Uzbekistan; durdiev65@mail.ru
U. D. Durdiev – Kazan Federal University, Kazan, Russia; umidjan93@mail.ru
We consider the problem of reconstructing the time-dependent history of the viscoelasticity medium from the viscoelasticity system of equations for an homogeneous anisotropic medium. As additional information, the Fourier image of the displacement vector for values ν = ν0 ≠ 0 of transformation parameter is given. It is shown that if the given functions satisfy some conditions of agreement and smoothness, the solution for the posed problem is uniquely defined in the class of a continuous functions and it continuously depends on given functions.
Keywords: inverse problem, integro-differential equation, delta function, Fourier transformation, agreement condition.
PACS 02.30.Zz
DOI 10.17586/2220-8054-2016-7-3-405-409