Global Classical Solutions To Cauchy Problem Of Quasilinear Hyperbolic Systems With Compact-supported Initial Data

In this paper, we study the Cauchy problem for quasi-linear hyperbolic systems of diagonal form and get the global existence and uniqueness on t≥0 when the derivative of the initial data has compact support and the system is strictly hyperbolic; and get the existence and uniqueness on the nth characteristic-determined area when the initial data has compact support. We mainly recruit the characteristic method and the uniform a priori estimate method.