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

T. D.Omurov; A. M.Alybaev

T. D.Omurov Z. Balasagyn Kyrgyz National University, Bishkek, Kyrgyzstan
A. M.Alybaev Department of Algebra, Geometry, Topology and Teaching of Higher Mathematics, Bishkek, Kyrgyzstan

Article ID: 2555

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

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.

References

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

[2]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.

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

[4]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.

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

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

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

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

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

[10]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.