广义Chaplygin气体Aw-Rascle交通流方程组解奇异性的形成  

Formation of Singularities in Solutions to the Aw-Rascle Traffic Flow System for the Generalized Chaplygin Gas

作　　者：辛晓庆 郭俐辉[1] XIN Xiaoqing;GUO Lihui(School of Mathematics and System Sciences,Xinjiang University,Urumqi Xinjiang 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,新疆乌鲁木齐830017

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第4期422-432,共11页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：国家自然科学基金“相对论欧拉方程组音速-超音速解的存在性及相关问题研究”(12161084);新疆维吾尔自治区自然科学基金“双曲型偏微分方程组初边值问题解的存在性”(2022D01E42).

摘　　要：研究了广义Chaplygin气体Aw-Rascle交通流方程组经典解奇异性的形成.利用特征分解方法,当初值满足一定条件时,证明了交通流模型柯西问题经典解的密度本身在有限时间内会发生爆破.此外,通过数值模拟对该物理现象进行了验证.The formation of singularities in the classical solutions to the Aw-Rascle traffic flow system with generalized Chaplygin gas is studied.By using the method of characteristic decomposition,we prove that the density itself of the classical solutions of the Cauchy problem for the traffic flow model will blow up in finite time when the initial data meets certain conditions.Additionally,this physical phenomenon is verified by numerical simulation.

关 键 词：Aw-Rascle交通流方程组 广义Chaplygin气体 奇异性的形成 特征分解 

分 类 号：O175.2[理学—数学]