Bulletin KRASEC. Phys. & Math. Sci, 2014, V. 9, №. 2, pp. 3-12. ISSN 2313-0156
ABOUT A METHOD OF RESEARCH OF THE NON-LOCAL PROBLEM FOR THE LOADED MIXED TYPE EQUATION IN DOUBLE-CONNECTED DOMAIN
National University of Uzbekistan by Mirzo Ulugbeka, 100174, Uzbekistan, Tashkent c., VUZ gorodok st.
In the present paper an existence and uniqueness of solution of the non-local boundary value problem for the loaded elliptic-hyperbolic type equation on the third order in double-connected domain was investigated. The uniqueness of solution was proved by the extremum principle for the mixed type equations, and existence was proved by the method of integral equations.
Key words: loaded equation, elliptic-hyperbolic type, double-connected domain, an extremum principle, existence of solution, uniqueness of solution, method of integral equations
- Nakhushev A.M. Nagruzhennye uravneniya i ih prilozheniya [The loaded equations and their applications]. Moscow, Nauka Publ., 2012. 232 p.
- Abdullaev O.Kh. Kraevaya zadacha dlya nagruzhennogo uravneniya ‘elliptiko-giperbolicheskogo tipa v dvusvyaznoj oblasti [Boundary value problem for a loaded equation elliptic-hyperbolic type in double connected domain]. Vestnik KRAUNC. Fiziko-matematicheskie nauki. — Bulletin KRASEC. Physical and Mathematical Sciences, 2014, no. 1(8), pp. 33-48.
- Bitsadze A.V. Differential equations of Mixed type. New York, Pergamon Press, 1964. 160 p. 4. `Iuskheleshvili N.I. Singulyarnye integral’nye uravneniya [Singularity integral equations]. Moscow, Nauka Publ., 1968. 512 p.
Original article submitted: 10.12.2014
Abdullayev Obidjon Khayrullaevich – Ph.D. (Phys. & Math.), Associate Professor Dept. of Differential equations of the National University of Uzbekistan named after Ulugbek, Tashkent, Uzbekistan.
Download article Abdulaev O.Kh.