Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas
Measure solutions of one-dimensional piston problem for compressible Euler equations of Chaplygin gas
复制标题
Chaplygin 气体可压缩欧拉方程一维活塞问题的测度解
DOI：
10.1016/j.jmaa.2019.123486
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发表时间：
2020
影响因子：
1.3
通讯作者：
Yuan Hairong
中科院分区：
文献类型：
--
作者：
Qu Aifang;Yuan Hairong
本文研究Chaubergin气体可压缩欧拉方程的一维活塞问题。如果活塞以恒定的亚音速运动到均匀气体中，则存在活塞问题的积分弱解，该积分弱解由分离活塞前方的恒定状态的激波组成。当活塞运动速度为音速或超音速时，则应引入奇异测度解，其密度包含一个支撑在活塞上的Dirac测度。当活塞以任意常速度离开气体，且不存在真空时，存在积分弱解。在活塞马赫数趋于无穷大的极端情况下，极限方程和解与多方气体的极限方程和解相同。
We are concerned with the one-dimensional piston problem for the compressible Euler equations of Chaplygin gas. If the piston moves at constant subsonic speed to the uniform gas, there exists an integral weak solution for the piston problem, consisting of a shock separating constant states ahead of the piston. While if the speed of the piston is sonic or supersonic, a singular measure solution, with density containing a Dirac measure supported on the piston, shall be introduced to solve the problem. Integral weak solution exists for the piston receding from the gas with any constant speed, and there is no vacuum. In the extreme case as the Mach number of the piston goes to infinity, the limiting equations and solutions are the same as that for the polytropic gases.