Advances in Differential Equations and Control Processes

The Advances in Differential Equations and Control Processes is an esteemed international journal indexed in the Emerging Sources Citation Index (ESCI). It publishes original research articles related to recent developments in both theory and applications of ordinary and partial differential equations, integral equations, and control theory. The journal highlights the interdisciplinary nature of these topics, with applications in physical, biological, environmental, and health sciences, mechanics, and engineering. It also considers survey articles that identify future avenues of advancement in the field.

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REGULARIZATION OF A SYSTEM OF THE FIRST KIND VOLTERRA INCORRECT TWO DIMENSIONAL EQUATIONS

Authors

  • T. D. Omurov
  • A. M. Alybaev

Keywords:

regularization method (RM), small parameter, special solution, ill‑posed problem, system of the first kind Volterra integral equations (SVIE-1).

DOI:

https://doi.org/10.17654/0974324322018

Abstract

In this paper, we study a system of the first kind Volterra incorrect integral equations. On the basis of the developed method of asymptotic nature with a singular function with respect to a small parameter, the regularizability and uniqueness of the solution of the original system in the introduced space are proved.

Received: February 25, 2022
Revised: March 30, 2022
Accepted: April 2, 2022

References

A. S. Apartsin, Non-classical Volterra equations of the 1st kind: theory and numerical methods, Novosibirsk, Science, 1999, p. 199.

D. S. Anikonov, On the question of the uniqueness of the solution of inverse problems for equations of mathematical physics, Differ. Equations 1 (1979), 3-9.

A. L. Bukhgeim, Volterra equation and inverse problems, Novosibirsk, Science, 1983, p. 207.

A. M. Denisov, On the approximate solution of the Volterra equation of the first kind associated with one inverse problem for the heat equation, West Moscow State University, Vychisl. Mat. and Cybern. 3 (1980), 49-52.

M. I. Imanaliev, Generalized solutions of integral equations of the first kind, Frunze, Ilim, 1981, p. 144.

M. M. Lavrent’ev, Integral equations of the first kind, Report of the Academy of Sciences of the USSR 127(1) (1959), 31-33.

T. D. Omurov, Regularization methods for Volterra integral equations of the first and third kind, Bishkek, Ilim, 2003, p. 162.

V. O. Sergeev, Regularization of the first kind Volterra equations, DAN SSSR 197(3) (1971), 531-534.

A. N. Tychonov and V. Y. Arsenin, Methods for Solving Ill-posed Problems, Nauka, 1986, p. 287.

Ten Myung Yang, Approximate solution of the first kind Volterra two-dimensional integral equations by the quadrature method, Differential and Integral Equations 3 (1975), 194-211.

Published

2022-05-10

Issue

Section

Articles

How to Cite

REGULARIZATION OF A SYSTEM OF THE FIRST KIND VOLTERRA INCORRECT TWO DIMENSIONAL EQUATIONS. (2022). Advances in Differential Equations and Control Processes, 27, 149-162. https://doi.org/10.17654/0974324322018

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