Global weakly discontinuous solutions for hyperbolic conservation laws in the presence of a boundary ✩

This work is a continuation of our previous work, in the present paper we study the mixed initial-boundary value problem for general n × n quasilinear hyperbolic systems of conservation laws with non-linear boundary conditions in the half space {(t, x) | t 0, x 0}. Under the assumption that each characteristic with positive velocity is linearly degenerate, we prove the existence and uniqueness of global weakly discontinuous solution u = u(t, x) with small amplitude, and this solution possesses a global structure similar to that of the self-similar solution u = U(xt ) of the corresponding Riemann problem. Some applications to quasilinear hyperbolic systems of conservation laws arising in physics and other disciplines, particularly to the system describing the motion of the relativistic string in Minkowski space R1+n, are also given