GLOBAL CLASSICAL SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR INHOMOGENEOUS QUASILINEAR HYPERBOLIC SYSTEMS

摘要

In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t,x): t ≥ 0, χ ≥ 0} is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a C~1 solution and its L~1 stability with certain small initial and boundary data.