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

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 View the MathML sourceu=U(xt), containing only shocks and contact discontinuities, of general n×nn×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the existence and uniqueness of global piecewise C1C1 solution containing only shocks and contact discontinuities to a class of the mixed initial-boundary-value-problem for general n×nn×n quasilinear hyperbolic systems of conservation laws in the half space {(t,x)|t≥0,x≥0}{(t,x)|t≥0,x≥0}. Our result indicates that this kind of Riemann solution View the MathML sourceu=U(xt) mentioned above for general n×nn×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.