Instability in Fermi-Ulam `ping-pong' problem
Instability in Fermi-Ulam `ping-pong' problem
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DOI：
10.1088/0951-7715/11/6/003
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发表时间：
1998-11
期刊：
影响因子：
1.7
通讯作者：
V. Zharnitsky
中科院分区：
文献类型：
--
作者：
V. Zharnitsky
考虑了经典粒子在两个平行壁之间弹性弹跳的运动，其中一个平行壁经历了周期运动。这个问题称为Fermi-Ulam‘ping-pong’，已知只有当墙的运动足够光滑时才有有界解，其中p(T)是墙的位置。给出了两个不稳定的例子，证明了当p(T)是连续函数时，稳定性结果不成立。第二个例子也回答了Levi M和Zehnder E(1995)中提出的问题：拟周期位势的解的有界性。肛门。261233-56)关于‘壁球运动员’的不稳定问题。这两个示例都是为具有不动墙的等效系统构建的。利用热方程理论中发展起来的变换来求解移动边界问题，得到了约化系统。
The motion of a classical particle bouncing elastically between two parallel walls, with one of the walls undergoing a periodic motion is considered. This problem, called Fermi-Ulam `ping-pong', is known to possess only bounded solutions if the motion of the wall is sufficiently smooth , where p(t) is the position of the wall. It is shown that the stability result does not hold if p(t) is just a continuous function by providing two examples of instability. The second example also answers the question posed in Levi M and Zehnder E (1995 Boundedness of solutions for quasiperiodic potentials SIAM J. Math. Anal. 26 1233-56) about instability in the `squash player's' problem. Both examples are constructed for an equivalent system with motionless walls. The reduced system is obtained using the transformation, developed in the heat equation theory to solve the moving boundary problem.