Global structure stability of Riemann solutions for general hyperbolic systems of conservation laws in the presence of a boundary

Abstract

This work is a continuation of our previous work [Z.-Q. Shao, Global structure instability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws in the presence of a boundary, J. Math. Anal. Appl. 330 (1) (2007) 511-540]. In the present paper, we study the global structure stability of the Riemann solution u = U ( x t ) , containing only shocks and contact discontinuities, of general n × n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the existence and uniqueness of global piecewise C 1 solution containing only shocks and contact discontinuities to a class of the mixed initial-boundary-value-problem for general n × n quasilinear hyperbolic systems of conservation laws in the half space { ( t , x ) | t ≥ 0 , x ≥ 0 } . Our result indicates that this kind of Riemann solution u = U ( x t ) mentioned above for general n × n quasilinear hyperbolic systems of conservation laws in a half space possesses a global structural stability. Some applications to quasilinear hyperbolic systems of conservation laws arising in physics and other disciplines are also given.