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

summary:In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant $\{(t,x)\colon t \geq 0, x \geq 0\}$ 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