BOUNDARY VALUE PROBLEMS FOR MIXED-TYPE DIFFERENTIAL EQUATIONS OF THE FIRST AND SECOND ORDER WITH RESPECT TO THE TIME VARIABLE
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1. Bers, L., Mathematical Problems of Subsonic and Transonic Gas Dynamics. Moscow: Foreign Literature
Publishing House, 1961. - 206 p.
2. Kuzmin A.G., Nonclassical Equations of Mixed Type and Their Applications in Gas Dynamics. Leningrad:
Leningrad State University Publishing, 1990. - 280 p.
3. Frankl F.I., Selected Works on Gas Dynamics. Moscow: Nauka, 1973. - 711 p.
4. He Kan Cher., The Singular Tricomi Problem for Equations of Mixed Type with Two Degeneracy Lines:
PhD Thesis in Physical and Mathematical Sciences. Novosibirsk, 1976.
5. Sabitov, K.B., Karamova, A.A., Spectral Properties of Solutions to the Tricomi Problem for a
Mixed-Type Equation with Two Type-Changing Lines and Their Applications. Izvestiya RAN. Seriya
Matematicheskaya, 2001. Vol. 65, No. 4, pp. 133-150.
6. Fayazov, K.S., An Ill-posed Boundary Value Problem for a Second-Order Equation of Mixed Type. Uzbek
Mathematical Journal, 1995, No. 2, pp. 89-93.
7. Fayazov K.S., Khajiev I.O., Fayazova Z.K., Ill-posed Boundary Value Problem for Operator-Differential
Equation of Fourth Order. Bulletin of National University of Uzbekistan: Mathematics and Natural
Sciences, 2018, Vol. 1, Issue 2, Article 3.
8. Fayazov K.S., Khudaybergenov Y.K., Ill-posed Boundary Value Problem for a System of Mixed-Type
Equations with Two Degeneracy Lines. Siberian Electronic Mathematical Reports, 2020, Vol. 17, pp.
647-660.
9. Lavrent‘ev M.M.,Saveliev L.Y., Theory of operators and ill-posed problems., Publishing House of the
Institute of Mathematics, Novosibirsk, 2010.
10. Krein M. G., Gohberg I. T., Introduction to the Theory of Linear Non-Self-Adjoint Operators in Hilbert
Space. Moscow: Nauka, 1965, 448 pages.
11. Pyatkov S. G., Some Properties of Eigenfunctions and Associated Functions of Indefinite Sturm-Liouville
Problems. In: Nonclassical Equations of Mathematical Physics: Collected Scientific Works. Novosibirsk:
Institute of Mathematics Publishing, 2005, pp. 240-251.
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