Two linearized models for a hyperbolic free boundary value problem

Abstract

We consider two linearized models which describe the motion of a gas in a cylinder with a piston at one end whose motion is determined by the pressure of the gas within the cylinder and by external forces. In the first model all second and higher order terms are neglected, whereas in the second model a quadratic correction term is added to the equation of motion of the piston so that energy arguments become applicable. For both models existence and uniqueness theorems are given.