Global classical solutions of mixed initial-boundary value problem for quasilinear hyperbolic systems

Abstract

In this paper, we consider the mixed initial-boundary value problem for quasilinear hyperbolic systems with nonlinear boundary conditions in the first quadrant { ( t , x ) | t ≥ 0 , x ≥ 0 } . Under the assumptions that the system is strictly hyperbolic and linearly degenerate or weakly linearly degenerate, the global existence and uniqueness of C 1 solutions are obtained for small initial and boundary data. We also present two applications for physical models.