The Research Of The Riemann Solution And It Stability For The Nonsymmetric Keyfitz-Kranzer Equations

In this paper,we first studied the Riemann solution of inhomogeneous Non-symmetrical Keyfitz-Kranzer system for the generalized Chaplygin gas.Whereafter,we considered the stability of the Riemann solutions for the Non-symmetry Kevyfitz-Kranzer system with Chaplygin pressure.The first chapter introduces the research background,current situation,main con-tents and structure of this paper.In Chapter 2,we mainly study the Riemann problem of the generalized Chaplygin gas asymmetric Keyfitz-Kranzer equation system with friction term,and obtain the global structure of its Riemann solution.Riemann solution contains shock wave,sparse wave,contact discontinuity and delta-shock wave.Unlike homogeneous asymmetric Keyfitz-Kranzer equation system,it is the non-similar that Riemann solution of the inhomoge-neous asymmetric Keyfitz-Kranzer equation system.In the third chapter,we mainly study the stability of Riemann solutions of the homogeneous Chaplygin gas asymmetric Keyfitz-Kranzer equations.We constructively obtain the explicit expressions of solutions of different structures of the equations under a small local perturbation to the initial value of Riemann.Then,by making the perturbation parameters tend to zero,we obtain the Riemann solutions that is stanility.Finally,we prove that there is no mass concentration even if the initial value tends to be infinite with??0.