非对称Keyfitz-Kranzer系统的解的消失压力和流扰动极限
发布时间：2018-10-15 12:49
【摘要】：本文研究非对称Keyfitz-Kranzer系统的黎曼解在压力和流扰动消失下的极限.利用特征和相平面分析法,构造性地求解了相应系统的黎曼问题.进一步地,讨论了当压力和流扰动分别消失时,黎曼解的极限行为.第一章介绍非对称Keyfitz-Kranzer系统的研究现状以及本文的研究工作.第二章回顾零压流的狄拉克激波和真空状态解.第三章研究Keyfitz-Kranzer系统当压力消失时黎曼解的极限.我们首先证明,当压力消失时,Keyfitz-Kranzer系统包含激波和接触间断的黎曼解收敛到一个狄拉克激波,其传播速度和强度却不同于零压流的狄拉克激波；包含疏散波、接触间断以及非真空中间状态的黎曼解收敛到零压流的真空状态.其次,求解扰动的Keyfitz-Kranzer系统的黎曼问题,构造了4种不同结构的黎曼解.进而证明,当压力消失时,扰动的Keyfitz-Kranzer系统的包含两个激波的黎曼解趋于零压流的狄拉克激波解;包含两个疏散波的黎曼解趋于零压流的真空解.第四章讨论Keyfitz-Kranzer系统的消失流扰动极限.首先求解流扰动系统的黎曼问题,获得4种不同的黎曼解.其次证明,当流扰动消失时,包含两个激波的黎曼解收敛到一个狄拉克激波解,但是其传播速度和强度却不同于零压流的狄拉克激波；包含两个疏散波的黎曼解收敛到零压流的真空解.最后,我们研究扰动的Keyfitz-Kranzer系统的消失流扰动极限.在求解该模型的黎曼问题的基础上,我们证明,当流扰动消失时,扰动的Keyfitz-Kranzer系统的包含两个激波的黎曼解趋于狄拉克激波解；包含两个疏散波的黎曼解收敛到真空解.
[Abstract]:In this paper, we study the limit of Riemann solution of asymmetric Keyfitz-Kranzer system under the condition that the pressure and flow disturbances disappear. The Riemann problem of the corresponding system is solved structurally by using the method of characteristic and phase plane analysis. Furthermore, the limit behavior of Riemann solution is discussed when the pressure and flow disturbances disappear respectively. The first chapter introduces the research status of asymmetric Keyfitz-Kranzer system and the research work of this paper. In chapter 2, the Dirac shock wave and vacuum state solution of zero pressure flow are reviewed. In chapter 3, we study the limit of Riemann solution of Keyfitz-Kranzer system when the pressure disappears. We first prove that when the pressure disappears, the Riemann solution of the Keyfitz-Kranzer system containing shock waves and contact discontinuities converges to a Dirac shock wave, the propagation speed and intensity of which are different from those of the zero pressure current Dirac shock wave. The Riemann solution of contact discontinuity and non-vacuum intermediate state converges to the vacuum state of zero pressure flow. Secondly, the Riemann problem of perturbed Keyfitz-Kranzer system is solved, and four kinds of Riemann solutions with different structures are constructed. It is further proved that when the pressure disappears, the Riemann solution of the perturbed Keyfitz-Kranzer system tends to the Dirac shock solution with two shock waves, and the Riemann solution with two evacuation waves approaches the vacuum solution of the zero pressure flow. In chapter 4, the vanishing flow perturbation limit of Keyfitz-Kranzer system is discussed. Firstly, the Riemann problem of the flow perturbed system is solved, and four different Riemann solutions are obtained. Secondly, it is proved that when the flow disturbance disappears, the Riemann solution containing two shock waves converges to a Dirac shock solution, but its propagation velocity and intensity are different from those of zero pressure flow. The Riemann solution containing two open waves converges to the vacuum solution of zero pressure flow. Finally, we study the vanishing flow perturbation limit of perturbed Keyfitz-Kranzer systems. On the basis of solving the Riemann problem of the model, we prove that when the flow disturbance disappears, the Riemann solution of the perturbed Keyfitz-Kranzer system with two shock waves tends to the Dirac shock solution, and the Riemann solution containing two evacuation waves converges to the vacuum solution.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175
[Abstract]:In this paper, we study the limit of Riemann solution of asymmetric Keyfitz-Kranzer system under the condition that the pressure and flow disturbances disappear. The Riemann problem of the corresponding system is solved structurally by using the method of characteristic and phase plane analysis. Furthermore, the limit behavior of Riemann solution is discussed when the pressure and flow disturbances disappear respectively. The first chapter introduces the research status of asymmetric Keyfitz-Kranzer system and the research work of this paper. In chapter 2, the Dirac shock wave and vacuum state solution of zero pressure flow are reviewed. In chapter 3, we study the limit of Riemann solution of Keyfitz-Kranzer system when the pressure disappears. We first prove that when the pressure disappears, the Riemann solution of the Keyfitz-Kranzer system containing shock waves and contact discontinuities converges to a Dirac shock wave, the propagation speed and intensity of which are different from those of the zero pressure current Dirac shock wave. The Riemann solution of contact discontinuity and non-vacuum intermediate state converges to the vacuum state of zero pressure flow. Secondly, the Riemann problem of perturbed Keyfitz-Kranzer system is solved, and four kinds of Riemann solutions with different structures are constructed. It is further proved that when the pressure disappears, the Riemann solution of the perturbed Keyfitz-Kranzer system tends to the Dirac shock solution with two shock waves, and the Riemann solution with two evacuation waves approaches the vacuum solution of the zero pressure flow. In chapter 4, the vanishing flow perturbation limit of Keyfitz-Kranzer system is discussed. Firstly, the Riemann problem of the flow perturbed system is solved, and four different Riemann solutions are obtained. Secondly, it is proved that when the flow disturbance disappears, the Riemann solution containing two shock waves converges to a Dirac shock solution, but its propagation velocity and intensity are different from those of zero pressure flow. The Riemann solution containing two open waves converges to the vacuum solution of zero pressure flow. Finally, we study the vanishing flow perturbation limit of perturbed Keyfitz-Kranzer systems. On the basis of solving the Riemann problem of the model, we prove that when the flow disturbance disappears, the Riemann solution of the perturbed Keyfitz-Kranzer system with two shock waves tends to the Dirac shock solution, and the Riemann solution containing two evacuation waves converges to the vacuum solution.
【学位授予单位】：云南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O175
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