非齐次非对称Keyfitz-Kranzer气体方程组的Riemann问题  

The Riemann Problem for the Nonsymmetric Keyfitz-Kranzer Gas Equations with a Nonhomogeneous Term

作　　者：李舒琪 LI Shuqi(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,Xinjiang)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830046

出　　处：《四川师范大学学报（自然科学版）》2020年第6期787-794,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11401508和11461066)。

摘　　要：主要研究非齐次Chaplygin气体情形下非对称Keyfitz-Kranzer方程组的Riemann问题.首先引入一个新的变量把非齐次Chaplygin气体非对称Keyfitz-Kranzer方程组转化为守恒形式,随后利用特征分析法和相平面分析法得到守恒形式Riemann问题的整体结构,当Riemann初值满足某些特定条件时,其Riemann解中会出现δ激波.通过构造和利用广义Rankine-Hugoniot条件得到了δ激波的位置、传播速度和强度.然后研究非齐次Chaplygin气体非对称Keyfitz-Kranzer方程组,得到Riemann问题的δ激波解,并严格证明其在分布意义下弱解的存在性.In this paper,the Riemann problem for the one-dimensional nonsymmetric Keyfitz-Kranzer systems with a nonhomogeneous term for the Chaplygin gas is considered.We can reformulate the conservative Keyfitz-Kranzer gas equations by introducing a new velocity.It is shown that the delta shock wave appears in the Riemann solutions of the conservative form in some certain situations by characteristics analysis and phase-plane analysis.According to establishing the generalized Rankine-Hugoniot conditions of delta shock wave,we obtain the position,propagation speed and strength of delta shock.Then we return to the nonsymmetric Keyfitz-Kranzer systems with a nonhomogeneous term and obtain the delta shock wave,and strictly prove the existence of the weak solutions in the sense of distributions.

关 键 词：Chaplygin气体 非对称Keyfitz-Kranzer方程组 RIEMANN问题 δ激波 

分 类 号：O175.12[理学—数学]