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| 摘要: |
| 本文研究了延拓Chaplygin气体的黎曼解在流逼近极限过程中的集中现象和狄拉克激波的两种形成机制问题.利用相平面分析法和广义特征分析法，构造出了延拓Chaplygin气体的整体黎曼解，并获得了两个结果：当压力消失时，延拓Chaplygin气体的包含两个激波的解收敛到输运方程的狄拉克激波解；当压力项趋近于广义Chaplygin压力项时，延拓Chaplygin气体的包含两个激波的解收敛到广义Chaplygin气体的狄拉克激波解.结论推广到了延拓Chaplygin气体. |
| 关键词: 延拓Chaplygin气体 狄拉克激波 流逼近极限 黎曼解 输运方程 广义Chaplygin气体 |
| DOI： |
| 分类号:O175.27 |
| 基金项目: |
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| CONCENTRATION IN THE FLUX APPROXIMATION LIMIT OF RIEMANN SOLUTIONS TO THE EXTENDED CHAPLYGIN GAS EQUATIONS |
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ZHANG Qing-ling
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| Abstract: |
| In this paper, two kinds of occurrence mechanism on the phenomenon of concentration and the formation of delta shock waves in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations are analyzed. By phase plane analysis and generalized characteristic analysis, we construct the Riemann solution to the extended Chaplygin gas equations completely and obtain two results: on one hand, as the pressure vanishes, any two-shock Riemann solution to the extended Chaplygin gas equations tends to a δ-shock solution to the transportation equation; on the other hand, as the pressure approaches the generalized Chaplygin pressure, any two-shock Riemann solution tends to a δ-shock solution to the generalized Chaplygin gas equations, which generalize to the extended Chaplygin gas. |
| Key words: extended Chaplygin gas δ-shock wave flux approximation limit Riemann solutions transportation equations generalized Chaplygin gas |
