В. И. Романовский номидаги математика институти ҳузуридаги илмий даражалар берувчи dsc

 
 
The tasks of the research work.
Studying unique solvability and obtaining 
stability estimates for the solution of the initial-boundary value problem for a 
hyperbolic integro-differential equation with two and three dimensional kernel of 
the Investigation of the inverse problem of finding the special kernels by the 
solution of the direct problem known at the point x = 0. Formulation and study of 
the Cauchy problem for a system of viscoelastic equations in homogeneous 
anisotropic media. Studying the problem of determining the diagonal matrix kernel
from the system of viscoelastic equations. Obtaining theorems of existence, 
uniqueness, and stability estimates. The construction of a numerical method for 
determining the dependence of the dielectric constant of a layered medium on the 
time frequency in the system of equations of electrodynamics with memory. 
The object of the research 
work is hyperbolic convolution-type integro-
differential equations.
 
The scientific novelty of the research work is as follows: 
The unique solvability of the direct problem, which consists in determining 
the solution of the initial-boundary value problem for a hyperbolic integro-
differential equation of convolution type with two and three-dimensional 
convolution kernels, was investigated. The existence, uniqueness and conditional 
stability theorems of solving the inverse problems of finding the time and spatial 
variables depending kernel and the spatial part of the kernel of the integral term 
are proved.
 
The Cauchy problem for the system of viscoelastic equations in homogeneous 
anisotropic media is investigated. The problems of determining the diagonal matrix 
function from the system of viscoelastic equations are studied. The local unique 

---

54 
solvability theorems are proved and the conditional stability estimate for the 
solution of the inverse problem is established.
 
For a horizontally layered medium, a numerical method was constructed to 
determine the dependence of the dielectric constant on frequency from the 
Maxwell system of equations with memory.
 

---

55