Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems

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, x ? 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.