GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

摘要

In this paper, the mixed initial-boundary value problem for general first order quasi-linear hyperbolic systems with nonlinear boundary conditions in the domain D = {(t, x) | t ≥ 0,x ≥ 0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.