关于δ初值的Chaplygin压交通流AR模型的Riemann问题  

The Riemann Problem with Delta Initial Data for the Aw-Rascle Traffic Model with Chaplygin Pressure

作　　者：邵志强[1] 

机构地区：[1]福州大学数学与计算机科学学院,福州350116

出　　处：《数学物理学报（A辑）》2014年第6期1353-1371,共19页Acta Mathematica Scientia

基　　金：福建省自然科学基金(2012J01006)资助

摘　　要：研究Chaplygin压交通流AR模型初值含Dirac δ函数的Riemann问题.在广义Rankine-Hugoniot条件和熵条件下,构造性地获得了包含δ激波的整体广义解,明确地显示出四种不同的结构.结果表明,在Riemann初值这里构造的扰动下,Riemann解是稳定的.In this paper, we study the Riemann problem with the initial data containing the Dirae delta function for the Aw-Rascle traffic model with Chaplygin pressure. Under the generalized Rankine-Hugoniot relation and the entropy condition, we constructively obtain the global existence and uniqueness of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures. Moreover, it can be found that the solutions constructed here are stable for some perturbations of the initial data.

关 键 词：Chaplygin压交通流AR模型 RIEMANN问题 广义Rankine-Hugoniot条件 δ激波 熵条件 

分 类 号：O175.27[理学—数学]