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Boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. (English) Zbl 1145.35440
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:
35M10PDE of mixed type
35G15Boundary value problems for linear higher-order PDE