论文标题
用于修饰的chechlygin气体的等屈力Euler方程的活塞问题
Piston problem to the isentropic Euler equations for modified Chaplygin gas
论文作者
论文摘要
在本文中，我们针对修饰的Chaplygin气体的一维等速欧拉方程进行建设性地解决了活塞问题。在解决方案中，当活塞向前推进气体时，我们严格地证明了冲击波将恒定状态区分开的全球存在和唯一性。它与Chaplygin气体或广义Chaplygin气体的结果完全不同，其中构建了ra液溶液以处理活塞上的质量浓度。当活塞从气体中退回时，我们严格证实只有第一个家庭稀有波就存在于活塞前，而浓度永远不会发生。此外，通过研究限制行为，我们表明，经过修改的Chaplygin气体方程的活塞溶液倾向于将其作为压力态函数的单个参数消失。
In this paper, we solve constructively the piston problem for one-dimensional isentropic Euler equations of modified Chaplygin gas. In solutions, we prove rigorously the global existence and uniqueness of a shock wave separating constant states ahead of the piston when the piston pushed forward into the gas. It is quite different from the results of Chaplygin gas or generalized Chaplygin gas in which a Radon measure solution is constructed to deal with concentration of mass on the piston. When the piston pulled back from the gas, we strictly confirm only the first family rarefaction wave exists in front of the piston and the concentration will never occur. In addition, by studying the limiting behavior, we show that the piston solutions of modified Chaplygin gas equations tend to the piston solutions of generalized or pure Chaplygin gas equations as a single parameter of pressure state function vanishes.
