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Zbl 1145.35440
Eshmatov, B.E.; Karimov, E.T.
Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. (English)
[J] Cent. Eur. J. Math. 5, No. 4, 741-750 (2007). ISSN 1895-1074; ISSN 1644-3616/e

Summary: 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.

MSC 2000:: *35M10 PDE of mixed type
35G15 Boundary value problems for linear higher-order PDE

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

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Zentralblatt MATH Berlin [Germany]