论文标题
测量活塞问题的解决方案，以使其可压缩流体流量的普通流体流量
Measure solutions to piston problem for compressible fluid flow of generalized chaplygin gas
论文作者
论文摘要
我们研究了具有广义的Chaplygin气体的可压缩流体流动的活塞问题。根据马赫数的明显临界价值，我们证明，存在一个不可或缺的弱解决方案，对于诉讼活塞问题，如果马赫数小于此临界价值，则在持续的活塞之前将震动分开，而奇异的措施解决方案，而奇异的衡量解决方案的密度则包含在PISTON上的零件量子，则应提出与Mach数字相等的质量，即使在PISTON上支持Mach数字的范围更大。对于退化的活塞问题，当活塞以任何恒定速度从气体中退缩时，稀疏波解总是存在。此外，由于马赫数倾向于无穷大，在后退案例中分析了真空状态的发生和解决方案的收敛以及方程式的变性。
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.
