Global classical solutions to the initial-boundary value problem for diagonal quasilinear hyperbolic systems

Abstract This paper investigates the initial-boundary value problem for quasilinear strictly hyperbolic systems of diagonal form with characteristics which are partially linearly degenerate and partially weakly linearly degenerate. Furthermore, the study incorporates more sophisticated boundary conditions, including time t, offering a novel perspective for dealing with a broader spectrum of physical models. These findings substantiate the existence of global classical solutions under certain conditions and demonstrate the control of complex nonlinear interactions arising from the coexistence of degenerate and non-degenerate modes through precise energy estimation techniques.