一维简单活塞问题
A simple piston problem in one dimension
摘要：
我们研究了一个重活塞，它分离了在一维气室中运动的许多理想气体粒子。使用平均技术，我们证明了精确的速度收敛的实际运动的活塞，其平均行为。在紧集上，在所有初始条件下一致收敛。结果扩展了Sinai和Neishtadt的早期工作，他们确定了平均行为是周期振荡。此外，我们研究了活塞系统时，粒子的相互作用已被平滑。在初始条件和平滑量上，向平均行为的收敛再次均匀地发生。
英文摘要：
We study a heavy piston that separates finitely many ideal gas particles moving inside a one-dimensional gas chamber. Using averaging techniques, we prove precise rates of convergence of the actual motions of the piston to its averaged behavior. The convergence is uniform over all initial conditions in a compact set. The results extend earlier work by Sinai and Neishtadt, who determined that the averaged behavior is periodic oscillation. In addition, we investigate the piston system when the particle interactions have been smoothed. The convergence to the averaged behavior again takes place uniformly, both over initial conditions and over the amount of smoothing.
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