About One Non-Local Problem for The Degenerating Parabolic-Hyperbolic Type Equation

Abstract

In the present paper, the existence and uniqueness of solution of the analogue ofFrankl’s problem for the degenerated equation of the parabolic-hyperbolic type wasinvestigated. Uniqueness of solution of the investigated problem are proved withprinciple an extremum and existence of solution with method of integral equations

References

1. Bitsadze.A.V.Differetial equations of Mixed type. Mac Millan. co., New York. 19 Bitsadze.A.V. Some classes of partial differential equations. Gordon and Beach., New York. 1988.
2. Gel’fand I.M.: ”Some questions of analysis and differential equations”, UMN, ser.3 (87), Vol.XIV, (1959), pp.3-19.
3. Guo-chun Wen. H.Begehr. Existence of solutions of frankl problem for general Lavret’ev-Bitsadze equations. Revue Roumaine Math.Pure Apll.45 (2000), pp 141-160.
4. Ilin .. Kalashnikov A.S. Oleynik .. A linear parabolic type equation of the second order. Uspexi. mat.nauk.1962. V.17. pp.3-141.
5. Mikhlin S.G.Integralnie equations. ML Gitl, 1947. 304 p. 1973. 144.
6. Salakhitdinov .S. Mengziyayev B. Boundary value problems for one mixed type equation with two lines of degeneration. News N UzSSR. ser.phyz.mat.nauk. 19 Smirnov .. Mixed type equations. M.Nauka. 2000.
7. Rassias J.M. ” Mixed Type Partial Differential Equations With Initial and Boundary Values in Fluid Mechanics” International Journal of Applied Mathematics Statistics, Int. J. Appl. Math. Stat. June 2008. 77-107.
8. Tersenov S.A. Introduction in the theory of equations degenerating at the border. Novosibirsk.NGY. 1973. 144 p.