Mathematics – Dynamical Systems
Scientific paper
2006-12-14
Communications in Mathematical Physics 275 (2007), no. 2, 553-580
Mathematics
Dynamical Systems
33 pages, 3 figures
Scientific paper
We study a heavy piston of mass $M$ that separates finitely many ideal, unit mass gas particles moving in two or three dimensions. Neishtadt and Sinai previously determined a method for finding this system's averaged equation and showed that its solutions oscillate periodically. Using averaging techniques, we prove that the actual motions of the piston converge in probability to the predicted averaged behavior on the time scale $M^ {1/2} $ when $M$ tends to infinity while the total energy of the system is bounded and the number of gas particles is fixed.
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