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| 摘要: |
| 本文中，我们分析和研究了延拓Chaplygin气体黎曼解的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。首先，我们构造出了延拓Chaplygin气体的整体黎曼解。其次，我们严格证明了，当压力消失时，延拓Chaplygin气体的任何2-激波黎曼解收敛到输运方程的狄拉克激波解，其中间状态的密度收敛到一个狄拉克测度并形成狄拉克激波；延拓Chaplygin气体的任何2-稀疏波黎曼解收敛到输运方程的2-接触间断解，其非真空的中间状态收敛到真空状态。最后， 我们还证明了，当压力趋向于广义Chaplygin气体的压力时，延拓Chaplygin气体的任何2-激波黎曼解收敛到广义Chaplygin气体的狄拉克激波解。 |
| 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;O175.29 |
| 基金项目:武汉市教研项目（2017007） |
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| Concentration in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations |
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zhangqingling
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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 and identified. Firstly, the Riemann problem of the extended
Chaplygin gas equations is solved completely. Secondly, we rigorously show that, as the pressure vanishes,
any two-shock Riemann solution to the extended Chaplygin gas equations tends to a delta-shock solution
to the transportation equations, and the intermediate density between the two shocks tends to a weighted
delta-measure that forms the delta-shock; any two-rarefaction-wave Riemann solution to the extended
Chaplygin gas equations tends to a two-contact-discontinuity solution to the transportation equations,
and the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. At
last, we also show that, as the pressure approaches the generalized Chaplygin pressure, any two-shock
Riemann solution tends to a delta-shock solution to the generalized Chaplygin gas equations |
| Key words: Extended Chaplygin gas Delta shock wave flux approximation limit Riemann solutions Transportation equations generalized Chaplygin gas |
