REGULARIZATION METHOD IN CONDITIONALLY WELL-POSED INVERSE PROBLEMS DEGENERATING IN THE FIRST KIND VOLTERRA EQUATIONS
In the study of wide classes of inverse problems of mathematical physics, Volterra integral equations of the first kind with a special solution are degenerated. Therefore, the emphasis is placed on the regularization of these equations by means of weight functions that allow partial inversion of operators and make it possible to construct special solutions in special non-Banach spaces. The obtained results of the work can be applied to conditionally correct multidimensional inverse problems of the above-mentioned type. In this regard, studies of inverse problems of the above-mentioned type are relevant.
differential equations, conditionally well-posed problems, inverse problems, the first kind Volterra integral equations, regularization method.
Received: March 28, 2021; Accepted: April 8, 2021; Published: April 27, 2021
How to cite this article: A. M. Alybaev, Regularization method in conditionally well-posed inverse problems degenerating in the first kind volterra equations, Advances in Differential Equations and Control Processes 24(2) (2021), 187-198. DOI: 10.17654/DE024020187
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] M. M. Lavrent’ev, On Some Ill-posed Problems in Mathematical Physics, -Novosibirsk: Publishing House of the Siberian Branch of the USSR Academy of Sciences, 1962, p. 92 (in Russian).[2] A. N. Tychonov and V. Y. Arsenin, Methods for Solving Ill-posed Problems, Nauka, 1986, p. 287 (in Russian).[3] A. S. Apartsin, Non-classical Volterra Equations of the 1st Kind: Theory and Numerical Methods, Novosibirsk: Science, 1999, p. 199 (in Russian).[4] M. M. Lavrent’ev, Integral equations of the first kind, Report of the Academy of Sciences of the USSR 127(1) (1959), 31-33 (in Russian).[5] A. L. Bukhgeim, Volterra Equation and Inverse Problems, Novosibirsk: Science, 1983, p. 207 (in Russian).[6] V. I. Dmitriev, Inverse problems of electromagnetic methods of geophysics, Coll.: Ill-posed problems of natural science, -M.: MSU, 1987, p. 54-76 (in Russian).[7] V. G. Romanov, Inverse Problems for Differential Equations, -Novosibirsk: NSU, 1973, p. 225 (in Russian).[8] T. D. Omurov, Regularization Methods for Volterra Integral Equations of the First and Third Kind, Bishkek: Ilim, 2003, p. 162 (in Russian).[9] V. A. Trenogin, Functional Analysis, -M.: Nauka, 1980, p. 496 (in Russian).