The Existence Of The Global Classical Solutions To Quasilinear Hyperbolic Right-angle

In this paper, we study the first order quasilinear hyperbolic systems with two independent variables. They arise in many fields of Mechanics and Physics. Generally speaking, the classical solutions to the first order quasilinear hyperbolic systems only exist in a short time even for small initial data. Hence the problem: when does a global classical solution exist? In fact, there are theoretical and applied needs to study the global existence of classical solutions. Global existence of classical solutions is the prerequisite to the study of their global behaviors and numerical computations or simulations. Therefore it is of theoretical and practical interest to study the global existence of the classical solution to the first order quasilinear hyperbolic systems.As the special case, we consider the first order quasilinear hyperbolic systems of diagonal form with characteristics partly linearly degenerate and partly weakly linearly degenerate. The existence of global classical solution to the Cauchy problem for this kind of systems is obtained under appropriate assumption on the initial data.