中文摘要：

本文研究了初值导数具有紧支集的对角形严格双曲组Cauchy问题在t>0上的经典解的整体存在唯一性,以及在最大特征的决定区域内的较一般的非严格双曲组的初值是在x≥0半轴上给定的,并且初值具有紧支集的Cauchy问题的经典解的整体存在唯一性.文中主要使用了特征线方法和解的一致先验估计方法.

英文摘要：

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.