初值含Dirac函数的一个简化趋化性模型的Riemann问题  

Riemann Problem of a Simplified Chemotaxis Model with Dirac Functions in Initial Value

作　　者：孙寅酉 郭俐辉[1] 刘冬冬 SUN Yinyou;GUO Lihui;LIU Dongdong(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《吉林大学学报（理学版）》2023年第1期32-40,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12161084);新疆维吾尔自治区优秀青年基金(批准号:2019Q015)。

摘　　要：利用相平面分析法和广义Rankine-Hugoniot条件讨论一个含Dirac初值的简化趋化性模型的Riemann问题.根据初值q±,q0和0之间的大小关系,将问题分为5种情形讨论,并构造性地得到了该问题的全局解.最后,利用数值模拟验证理论结果的正确性.The Riemann problem of a simplified chemotaxis model with Dirac initial value was discussed by using phase-plane analysis method and generalized Rankine-Hugoniot conditions. According to the relationship between the initial values q±,q0and 0, we divided the Riemann problem into five cases and obtained the global solutions of the problem constructively. Finally, numerical simulations were used to verify the correctness of the theoretical results.

关 键 词：相平面分析 Rankine-Hugoniot条件 Dirac初值 趋化模型 数值模拟 

分 类 号：O175.22[理学—数学]