广义Chaubergin气体可压缩流动活塞问题的测度解
Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas
摘要：
本文研究了广义Chaubergin气体的可压缩流体活塞问题。根据推导出的马赫数临界值，证明了当马赫数小于该临界值时，活塞问题存在积分弱解，即在活塞前有一个分离定常状态的激波，而在活塞上有一个奇异测度解，其密度包含Dirac测度，当马赫数大于或等于临界值时，应提出一种解决活塞问题的方法。对于活塞后退问题，当活塞以任意等速后退时，稀疏波解总是存在的。在马赫数趋于无穷大的后退情形下，分析了真空态的出现、解的收敛性以及方程的退化性。
英文摘要：
We study the piston problem of the compressible fluid flow with the generalized Chaplygin gas. Depending on the inferential critical value of Mach number, we prove that, there exists an integral weak solution for the proceeding piston problem, consisting of a shock separating constant states ahead of the piston if Mach numbers less than this critical value, while a singular measure solution, with density containing a Dirac measure supported on the piston, shall be proposed to solve the proceeding piston problem if Mach numbers greater than or equal to the critical value. For the receding piston problem, rarefaction wave solution always exists when the piston recedes from the gas with any constant speed. Moreover, the occurrence of vacuum state and the convergence of solutions, as well as degeneration of equations are analyzed in the receding case as Mach number tends to infinity.
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