【摘要】：本文研究非對稱Keyfitz-Kranzer系統(tǒng)的黎曼解在壓力和流擾動消失下的極限.利用特征和相平面分析法,構(gòu)造性地求解了相應(yīng)系統(tǒng)的黎曼問題.進(jìn)一步地,討論了當(dāng)壓力和流擾動分別消失時,黎曼解的極限行為.第一章介紹非對稱Keyfitz-Kranzer系統(tǒng)的研究現(xiàn)狀以及本文的研究工作.第二章回顧零壓流的狄拉克激波和真空狀態(tài)解.第三章研究Keyfitz-Kranzer系統(tǒng)當(dāng)壓力消失時黎曼解的極限.我們首先證明,當(dāng)壓力消失時,Keyfitz-Kranzer系統(tǒng)包含激波和接觸間斷的黎曼解收斂到一個狄拉克激波,其傳播速度和強(qiáng)度卻不同于零壓流的狄拉克激波；包含疏散波、接觸間斷以及非真空中間狀態(tài)的黎曼解收斂到零壓流的真空狀態(tài).其次,求解擾動的Keyfitz-Kranzer系統(tǒng)的黎曼問題,構(gòu)造了4種不同結(jié)構(gòu)的黎曼解.進(jìn)而證明,當(dāng)壓力消失時,擾動的Keyfitz-Kranzer系統(tǒng)的包含兩個激波的黎曼解趨于零壓流的狄拉克激波解;包含兩個疏散波的黎曼解趨于零壓流的真空解.第四章討論Keyfitz-Kranzer系統(tǒng)的消失流擾動極限.首先求解流擾動系統(tǒng)的黎曼問題,獲得4種不同的黎曼解.其次證明,當(dāng)流擾動消失時,包含兩個激波的黎曼解收斂到一個狄拉克激波解,但是其傳播速度和強(qiáng)度卻不同于零壓流的狄拉克激波；包含兩個疏散波的黎曼解收斂到零壓流的真空解.最后,我們研究擾動的Keyfitz-Kranzer系統(tǒng)的消失流擾動極限.在求解該模型的黎曼問題的基礎(chǔ)上,我們證明,當(dāng)流擾動消失時,擾動的Keyfitz-Kranzer系統(tǒng)的包含兩個激波的黎曼解趨于狄拉克激波解；包含兩個疏散波的黎曼解收斂到真空解.
[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.
【學(xué)位授予單位】：云南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：O175

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本文編號：2272605