The Riemann Problem And Interaction Of Elementary Waves For The Nonsymmetric Keyfitz-Kranzer Equations

In this paper,we first considered the interaction of elementary waves for nonsymmet-rical Keyfitz-Kranzer system for the generalized and modified Chaplygin gas.Whereafter,we studied the Riemann problem of inhomogeneously nonsymmetrical Keyfitz-Kranzer system for the Chaplyign gas.Different from the solution of homogeneous equations,the Riemann solutions of inhomogeneous Keyfitz-Kranzer equations are no longer self-similar.In the first chapter,the research background and status of this thesis are introduced.Meanwhile,the context and structure of the thesis will be presented.In the second chapter,we study the interaction of elementary waves for nonsym-metrical Keyfitz-Kranzer system for the generalized and modified Chaplygin gas.The Riemann solutions for the generalized Chaplygin gas consist of R + J,S + J and delta shock wave,while the Riemann solutions for the modified Chaplygin gas consist of R+ J and S + J.By the method of characteristic analysis and the phase plane analysis,we constructively obtain the global Riemann solutions of the nonsymmetric Keyfitz-kranzer equations with the initial data consisting of three piecewise constant states and prove the stability of this Riemann solutions.In the third chapter,we mainly consider the Riemann problem of inhomegeneously nonsymmetrical Keyfitz-Kranzer system for the Chaplyign gas.Firstly,by introducing a new variable,we transform the inhomogeneous nonsymmetrical Keyfitz-Kranzer system into a form of conservation laws,Further,with the method of characteristic and phase analysis,we obtain the Riermann solutions of inhomegeneously nonsymmetrical Keyfitz-Kranzer system for the Chaplyign gas.When the Riemann initial data satisfies some certain conditions,delta shock wave occurs in the Riemann solutions.By the generalized Rankine Hugoniot conditions,the location,propagation speed and weight of the delta shock wave can be determined.