In this paper a mixed problem with integral boundary conditions for a high-order partial differential equation of mixed type is studying. The authors consider the equation
in the rectangle , where is bounded for a , and has bounded partial derivatives such that and , for . To this equation they add the initial conditions
the boundary conditions for , , for , , and integral condition
where and are known functions which satisfy the compatibility conditions given in the last three equations.
The existence and uniqueness of the solution are proved as the proof is based on energy inequality, and on the density of the range of the operator generated by the considered problem.