Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations

• Autorzy: B. Eshmatov , E. Karimov
• Języki publikacji: EN

Abstrakty

EN

In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations with two and three lines of changing type.

Słowa kluczowe

EN

Parabolic-hyperbolic type equations; gluing conditions; boundary value problems; integral equation; ”abc” method

Kategorie tematyczne

• 35M10: Equations of mixed type

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2007
• Tom: 5
• Numer: 4
• Strony: 741-750

Daty

wydano

2007-12-01

online

2007-12-01

Twórcy

autor

B. Eshmatov

• Karshi State University

autor

E. Karimov

• Uzbek Academy of Sciences

Bibliografia

• [1] G. Bateman and A. Erdelyi: Higher transcendental functions. Bessel functions, functions of parabolic cylinder, orthogonal polynomials (in Russian), Russian translation of extracts from Volume II of the original English edition (McGraw Hill, New York, 1953), Nauka, Moscow, 1966.
• [2] A.S. Berdyshev and E.T. Karimov: “Some non-local problems for the parabolich-yperbolic type equation with non-characteristic line of changing type”, Cent. Eur. J. Math., Vol. 4, (2006), no. 2, pp. 183–193. http://dx.doi.org/10.2478/s11533-006-0007-8
• [3] A. Friedman: Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964.
• [4] I.M. Gel’fand: “Some questions of analysis and differential equations” (in Russian), Uspehi Mat. Nauk, Vol. 14, (1959), no. 3, pp. 3–19.
• [5] N.Yu. Kapustin and E.I. Moiseev: “On spectral problems with a spectral parameter in the boundary condition” (in Russian), Differ. Uravn., Vol. 33, (1997), no. 1, pp. 115–119, 143.
• [6] E.T. Karimov: “About the Tricomi problem for the mixed parabolic-hyperbolic type equation with complex spectral parameter”, Complex Var. Theory Appl., Vol. 50, (2005), no. 6, pp. 433–440.
• [7] E.T. Karimov: “Non-local problems with special gluing condition for the parabolichyperbolic type equation with complex spectral parameter”, Panamer. Math. J., Vol. 17, (2007), no. 2, pp. 11–20.
• [8] M.L. Krasnov: Integral equations. Introduction to the theory (in Russian), Nauka, Moscow, 1975.
• [9] J.M. Rassias: Lecture notes on mixed type partial differential equations, World Scientific Publishing Co., Inc., Teaneck, NJ, 1990.
• [10] K.B. Sabytov: “On the theory of equations of mixed parabolic-hyperbolic type with a spectral parameter”, Differentsial’nye Uravneniya, Vol. 25, (1989), no. 1, pp. 117–126, 181–182.
• [11] M.S. Salakhitdinov and A.K. Urinov: Boundary value problems for equations of mixed type with a spectral parameter (in Russian), Fan, Tashkent, 1997.
• [12] A.G. Shashkov: System-structural analysis of the heat exchange proceses and its application, Moscow, 1983.
• [13] G.D. Tojzhanova and M.A. Sadybekov: “Spectral properties of an analogue of the Tricomi problem for an equation of mixed parabolic-hyperbolic type” (in Russian), Izv. Akad. Nauk Kazakh. SSR Ser. Fiz.-Mat., (1990), no. 5, pp. 48–52.

Identyfikatory

DOI

10.2478/s11533-007-0029-x