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

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Eshmatov B. , Karimov E.

Open Mathematics

2007

tom 5

nr 4

741-750

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.

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

100%

Berdyshev A. , Karimov E.

Open Mathematics

2006

tom 4

nr 2

183-193

In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.