Abstract
In the present paper, we study a boundary value problem for a mixed parabolic-hyperbolic type equation in a rectangular domain and prove the existence of the unique solution of this problem. In the theory of boundary value problems for second order mixed type equations usually two conjugation conditions are in use, in general. In this case, for the solvability of boundary value problems governed by mixed type equations containing a hyperbolic equation in a rectangular domain a certain condition (on the sizes of the sides of the rectangle) appears. However, in this paper, we give three conjugation conditions so that such condition does not appear.
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