Article Title

Conditional Correctness and Approximate Solution of The Ill-Posed Boundary Value Problem for A System of Mixed Type Third Order Equations

Authors

K.S. Fayazov, Turin Polytechnic University, Kichik Halka yuli 17, Tashkent 100095, Uzbekistan.Follow
I.O. Khajiev, National University of Uzbekistan, Universitet Str. 4, Tashkent 100174, Uzbekistan.Follow

Abstract

In this paper, we consider a system of the mixed type third-order equations. A priori estimate for the solution of the problem under consideration is obtained. Theorems of uniqueness and conditional stability on a set of correctness have been proved. The approximate solution by the regularization method has been constructed

First Page

52

Last Page

59

References

[1]. Sabitov K.B. On the theory of mixed type equations.-M.: Fizmatlit, 2014.

[2]. Kuzmin A.G. Nonclassical Equation of Mixed Type and their Applications in Gas Dynamics. Leningrad State University, 1990.

[3]. Larkin N.A., Novikov V.A., Yanenko N.N. Nonlinear equation of variable type. -Novosibirsk, Nauka, Sib. Department, 1983. - 269 p.

[4]. Levine H. A. Logarithmic Convexity and the Cauchy Problem for some Abstract Second order Differential Inequalities // Journal of Dif. Equations -1970. -V.8. -P. 34-55.

[5]. Fayazov K.S. An ill-posed boundary-value problem for a second-order mixed-type equation // Uzbek. Math. J. -1995. № 2. -P. 89-93.

[6]. Fayazov K.S. and Khajiev I.O. Conditional correctness of boundary-value problem for a composite fourth-order differential equation // Izvestiya vuzov, Mathematics, RAS. -2015. -№ 4. -P. 65-75.

[7]. Fayazov K.S., Khajiev I.O. Conditional stability of theboundary value problem for a system of second-order abstract differential equations with operator coefficients. Uzbek Math. J., 2017, № 2, p. 145-155.

[8]. Pyatkov S.G. Properties of eigenfunctions of a certain spectral problem and their applications // Some Applications of Functional Analysis to Equations of Mathematical Physics, Inst. Mat. Novosibirsk, 1986. P.~65-84.

[9]. Pyatkov S.G., Abasheieva N.L. Solvability of boundary value problems for operator-differential equations of mixed type // Sib. Mat. J. 2000. Vol. 41, № 6. P. 1419-1435.

[10]. Pyatkov S. G. Properties of eigenfunctions of a certain spectral problem and their applications. Some Applications of Functional Analysis to Equations of Mathematical Physics, Inst. Mat., Novosibirsk, 1986. -P. 65-84.

Recommended Citation

Fayazov, K.S. and Khajiev, I.O. (2019) "Conditional Correctness and Approximate Solution of The Ill-Posed Boundary Value Problem for A System of Mixed Type Third Order Equations," Acta of Turin Polytechnic University in Tashkent: Vol. 9 : Iss. 1 , Article 1.
Available at: https://uzjournals.edu.uz/actattpu/vol9/iss1/1