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

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

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

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  • 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.
  • Gel’fand I.M.: ”Some questions of analysis and differential equations”, UMN, ser.3 (87), Vol.XIV, (1959), pp.3-19.
  • 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.
  • Ilin .. Kalashnikov A.S. Oleynik .. A linear parabolic type equation of the second order. Uspexi. mat.nauk.1962. V.17. pp.3-141.
  • Mikhlin S.G.Integralnie equations. ML Gitl, 1947. 304 p. 1973. 144.
  • 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.
  • 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.
  • Tersenov S.A. Introduction in the theory of equations degenerating at the border. Novosibirsk.NGY. 1973. 144 p.