Global Solution to the Generalized Riemann Problem in the Presence of a Boundary and Contact Discontinuities

Abstract

This work is a continuation of our previous work. In the present paper we study the global structure stability of the Riemann solution \(u=U(\frac{x}{t})\) containing only contact discontinuities for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary. We prove the existence and uniqueness of a global piecewise C1 solution containing only contact discontinuities to a class of the generalized Riemann problems for general n×n quasilinear hyperbolic systems of conservation laws in a half space. Our result indicates that this kind of Riemann solution \(u=U(\frac{x}{t})\) mentioned above for general n×n quasilinear hyperbolic systems of conservation laws in the presence of a boundary possesses a global nonlinear structure stability. Some applications to quasilinear hyperbolic systems of conservation laws occurring in physics and other disciplines, particularly to the system describing the motion of the relativistic string in Minkowski space R1 + n, are also given.