Characteristic Method And Generalized Riemann Problem Of Inviscid Burgers Equation

In this paper,we study the well-posedness of solutions to initial value problems of first order quasilinear ordinary differential equations and the generalized Riemann problem of inviscid Burgers equation.First,we obtain the existence and uniqueness of the initial value solutions of the first order quasilinear ordinary differential equations by using the contrac-tion mapping principle of ordinary differential equations and the compactness criterion of Ascoli-Arzela.Secondly,we consider that if(?)is continuous with respect to t and u on(0,T)(where T satisfies T<T0<1/A5(||?*||)),the initial value problem of the quasilinear ordinary differential equations has a unique and stable C1 solution on(0,T);Further,If(?)is Holder continuous with respect to t and u on(0,T),the initial value problem of the quasilinear ordinary differential equations has a unique and stable C1,? solution on(0,T).Finally,we consider the generalized Riemann problem of inviscid Burgers equation.We obtain that the measure solution of this problem does not contain a Dirac measure when t>0.