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. Supported by the National Natural Science Foundation of China (No. 10531020), the National Basic Research Program of China 2006CB805902, the Doctorial Foundation of National Educational Ministry 20050246001 and the 111 Project.