带有含时组合源项的输运方程的黎曼问题  

Riemann problem to the transport equations with time-dependent composite source terms

作　　者：韦晓跃 吴金柱 张宇 WEI Xiao-yue;WU Jin-zhu;ZHANG Yu(School of Mathematics,Yunnan Normal University,Kunming 650500,China;Yunnan Key Laboratory of Modern Analytical Mathematics and Applications,Kunming 650500,China)

机构地区：[1]云南师范大学数学学院,云南昆明650500 [2]云南省现代分析数学及其应用重点实验室,云南昆明650500

出　　处：《西南民族大学学报（自然科学版）》2024年第5期566-574,共9页Journal of Southwest Minzu University(Natural Science Edition)

基　　金：国家自然科学基金(12361048);云南省基础研究计划项目(202401AT070130);云南省教育厅科学研究基金项目(2024Y158)。

摘　　要：求解带有含时组合源项的输运方程的黎曼问题.首先,引入某个较一般的含时变量替换将非齐次含源系统转化为守恒律系统,并在守恒律框架下构造了包含δ-激波和真空的黎曼解.其次,借助适当的广义Rankine-Hugoniot条件和熵条件,建立了δ-激波解的存在唯一性.结果表明,受源项影响,系统的黎曼解不再自相似,且所有的特征线均变为曲线.数值模拟证实了理论分析.The Riemann problem to the transport equations with time-dependent composite source terms was solved.First,a more general time-dependent variable transformation was introduced to rewrite the non-homogeneous system with source terms into a system of conservation laws,and the Riemann solution containingδ-shock and vacuum was constructed in the framework of conservation laws.Then,by virtue of the suitable generalized Rankine-Hugoniot relation and entropy condition,the existence and uniqueness ofδ-shock wave solution was established.The results showed that,influenced by the source terms,the Riemann solution of the system was no longer self-similar and all the characteristic lines became curves.Numerical simulation confirmed the theoretical analysis.

关 键 词：输运方程 组合源项 黎曼问题 δ-激波 真空 数值模拟 

分 类 号：O186.12[理学—数学]