The Global Existence And Rupture Of The Classical Solutions Of Quasi-linear Hyperbolic Equations

This paper mainly studies the first order quasilinear strict hyperbolic systems cauchy problem in which the characteristic are distinct,and the initial data of the cauchy problem possesses certain decay properties as |x| ? +?.Under the assumption that the characteristic is weakly linear degenerate,the Cauchy problem has unique classical solutions.Under the assumption that the characteristic is not weakly linear degenerate,the classical solution of the Cauchy problem must blow up in a finite time.According to the content,this article is divided into the following four chapters:The first chapter introduces the introduction and main results of this thesis.The second chapter introduces some basic knowledge about this thesis.In the third chapter,we prove the global existence of classical solution of Cauchy problem.In the fourth chapter,we prove the blow-up phenomenon and life span of the classical solution.