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
. Sabitov K.B. On the theory of mixed type equations.-M.: Fizmatlit, 2014. . Kuzmin A.G. Nonclassical Equation of Mixed Type and their Applications in Gas Dynamics. Leningrad State University, 1990. . Larkin N.A., Novikov V.A., Yanenko N.N. Nonlinear equation of variable type. -Novosibirsk, Nauka, Sib. Department, 1983. - 269 p. . 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. . Fayazov K.S. An ill-posed boundary-value problem for a second-order mixed-type equation // Uzbek. Math. J. -1995. № 2. -P. 89-93. . 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. . 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. . 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. . 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. . 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.
Fayazov, K.S. and Khajiev, I.O.
"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
, Article 1.
Available at: https://uzjournals.edu.uz/actattpu/vol9/iss1/1