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

Open Mathematics (2007)

- Volume: 5, Issue: 4, page 741-750
- ISSN: 2391-5455

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topB. Eshmatov, and E. Karimov. "Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations." Open Mathematics 5.4 (2007): 741-750. <http://eudml.org/doc/269250>.

@article{B2007,

abstract = {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.},

author = {B. Eshmatov, E. Karimov},

journal = {Open Mathematics},

keywords = {Parabolic-hyperbolic type equations; gluing conditions; boundary value problems; integral equation; ”abc” method; local and non-local boundary value problems; ``abc'' method; two and three lines of changing type},

language = {eng},

number = {4},

pages = {741-750},

title = {Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations},

url = {http://eudml.org/doc/269250},

volume = {5},

year = {2007},

}

TY - JOUR

AU - B. Eshmatov

AU - E. Karimov

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

JO - Open Mathematics

PY - 2007

VL - 5

IS - 4

SP - 741

EP - 750

AB - 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.

LA - eng

KW - Parabolic-hyperbolic type equations; gluing conditions; boundary value problems; integral equation; ”abc” method; local and non-local boundary value problems; ``abc'' method; two and three lines of changing type

UR - http://eudml.org/doc/269250

ER -

## References

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- [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 Zbl1098.35116
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- [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. Zbl1144.35450
- [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. Zbl0728.35074

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