On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary (Q1079722)

Several initial-boundary value problems of equations describing the one- dimensional motion of the ideal polytropic gas are discussed. In our problems the gas is put into the region where the ends are not fixed, so the (specific) volume of the gas may grow infinitely as time increases. In the article the above conjecture is shown, that is, the temporally global existence of the unique and classical solutions and the growth of the (specific) volume of the gas under some assumptions are proved. To be precise, at least under the assumption guaranteeing the global existence of the solution, the upper limit of the volume of the gas tends to infinity as time increases. Moreover, adding some (not so strong) assumptions, the (specific) volume tends to infinity, and we can find the upper and lower bounds of the order of growth.