非对称Keyfitz-Kranzer方程组在压力消失过程中的质量集中和空化现象  

Concentration and Cavitation Phenomena for Nonsymmetric Keyfitz-Kranzer Type in the Vanishing Pressure

作　　者：方艳红 郭俐辉[1] FANG Yanhong;GUO Lihui(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）》2021年第5期605-614,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11401508,11761068,11961063);新疆维吾尔自治区自然科学基金(2017D01C053,2019D01C080)。

摘　　要：研究扩展Chaplygin气体非对称Keyfitz-Kranzer方程组在压力消失过程中黎曼解的极限行为.压力消失过程中,Keyfitz-Kranzer方程组包括激波和接触间断的黎曼解收敛到一类特殊的δ激波,其传播速度和权明显不同于零压流的δ激波.为解决此问题,引入扰动Keyfitz-Kranzer方程组并证明压力消失过程中,它的解收敛到零压流.最后,呈现一组具有代表性的数值实验来验证δ激波和真空状态的形成.This article is devoted to the study of the limit behavior for Keyfitz-Kranzer type in the vanishing pressure.The Riemann solution containing shock wave and contact discontinuity converges to a specialδshock wave whose propagation velocity and strength are different from theδshock wave of pressureless gas dynamics.To solve the problem,we introduce perturbed Keyfitz-Kranzer type,and then prove that the Riemann solution tends to zero pressure flow in the process of vanishing pressure.Finally,we present a group of representative numerical experiments to verify the formation ofδshock wave and vacuum states.

关 键 词：扩展Chaplygin气体 非对称Keyfitz-Kranzer方程组 零压流 δ激波 真空状态 

分 类 号：O175.[理学—数学]