The Generalized Riemann Problem For Chaplygin Nonsymmetric Keyfitz-Kranzer System With A Source Term

In this thesis,we first consider the Riemann problem with delta initial data for Chap-lygin nonsymmetric Keyfitz-Kranzer equations with a Coulomb-like friction term.Fur-thermore,the interaction of waves for the Chaplygin nonsymmetric Keyfitz-Kranzer e-quations with a source term are discussed.As a result of the influence of the source term,the Riemann solutions of Chaplygin nonsymmetric Keyfitz-Kranzer equations with a source term are no longer self-similar.The lines of all contact discontinuities and delta shock waves are curves.This thesis is divided into the following three chapters:The first chapter mainly introduces the research background and development situa-tion of nonsymmetric Keyfitz-Kranzer equations,as well as the research work and struc-ture framework of this thesis.The second chapter is mainly concerned with the generalized Riemann problem for Chaplygin nonsymmetric Keyfitz-Kranzer equations.Firstly,the delta initial data was given,and then the generalized Rankine-Hugoniot and entropy conditions were used to obtain the generalized solution structurally.The Riemann solution was composed of con-tact discontinuity,delta shock wave and delta contact discontinuity.In the third chapter,the wave interaction of the nonsymmetric Keyfitz-Kranzer e-quations with source term of Chaplygin gas is discussed.Firstly,the initial value of the disturbance Riemann of three pieces of constant state is given.And then using the charac-teristic analysis and the results of chapter 2,we constructively obtain the global solutions under seven different conditions.