Quasilinear Hyperbolic System Of Nonsmooth Initial Data Of The Singularity

Generally speaking, the classical solutions to the first order quasilinear hy-perbolic systems only exist in a short time even for small initial data and thesingularity will occur. Therefore it is theoretical and practical interest to studythe global existence of the classical solution and the life span to the first orderquasilinear hyperbolic systems.In this paper, we consider the Cauchy problem of the first order homogeneousstrictly hyperbolic systems with a kind of non-smooth initial data:which isgenuinely nonlinear:By using the characteristic method and the uniform a priori estimate method weobtain the formation of singularities of weakly discontinuous solutions and showthe estimate of the life span.