The setting of boundary conditions for boundary value problems of hyperbolic-elliptic coupled systems

This paper is devoted to the study of the proper setting of the boundary conditions for the boundary value problems of the hyperbolic-elliptic coupled systems of first order. The wellposedness of the corresponding boundary value problems is also established. The Lopatinski conditions for the boundary value problems of the elliptic systems is then extended to the case for hyperbolic-elliptic coupled systems. The result in this paper can be applied to the Euler system in fluid dynamics, especially to give wellposed boundary value problems describing subsonic flow.