Boundary value problem for a parabolic-hyperbolic equation in a rectangular domain

Abstract

In present paper we study a boundary value problem for a mixed parabolic-hyperbolic type equation in a rectangular domain and prove the existence of unique solution of this problem. In theory of boundary value problems for second order mixed type equations usually two conjugation conditions are in use. In this case, for mixed type equations containing hyperbolic equation in a rectangular domain for solvability of boundary value problem appears certain condition. In this paper we give three conjugation conditions. In this case mentioned condition not appears.