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

TL;DR

This paper investigates a boundary value problem for a mixed parabolic-hyperbolic equation in a rectangular domain, establishing the existence and uniqueness of solutions using three conjugation conditions, which simplifies the solvability criteria.

Contribution

The paper introduces a boundary value problem with three conjugation conditions for mixed type equations, eliminating the need for a solvability condition.

Findings

Proved existence and uniqueness of solutions.

Established that three conjugation conditions suffice.

Simplified the solvability criteria for mixed type equations.

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.