The Classical Solution Of The Cauchy Problem To Inhomogeneous First Order Quasilinear Hyperbolic Systems

This thesis mainly investigates the global existence of the classical solution of the Cauchy problem to first order quasilinear hyperbolic systems with the inhomogeneous term as F(t,x).First of all, a brief introduction of the basic assumptions and the history on the study of the Cauchy problem to first order quasilinear hyperbolic systems is given in Chapter1.For convenience, in Chapter2, we list the definition of strictly row-diagonally dominant, and popularize the definition of strictly row-diagonally dominant to function matrix. Besides, we use a new method to give a refine formulas on the decomposition of waves of first order quasilinear hyperbolic systems with inhomogeneous term.In Chapter3, first we give the main results obtained in this thesis, and then, with the help of the formulas on the decomposition of waves and the preliminaries in Chapter2, we prove the global existence of the classical solution of the Cauchy problem to first order quasilinear hyperbolic systems with the inhomogeneous term as F(t, x).