On the Piston problem in gasdynamics (Q1067526)

In a preceding paper [The moving load on a string as free boundary problem (to be published)] the author treated a free boundary problem concerning the moving load on a string; now he uses his method to the resolution of this typical example of a free boundary problem in gasdynamics. That means he treats the question for the linearized equations of an isentropic fluid subject to external forces. First the physico-mathematical problem is stated and the equations are suitably transformed. Then the free boundary problem is precisely formulated, where some useful definitions are also given. After that, by adapting the methodology of the author's above mentioned work, there is shown a uniqueness and existence theorem which solves completely the problem and permits to have the solution in an explicit form. Finally, a particular case is studied.