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On the one-dimensional motion of the polytropic ideal gas non-fixed on the boundary. (English) Zbl 0598.34021
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.

MSC:
34B99 Boundary value problems for ordinary differential equations
35B40 Asymptotic behavior of solutions to PDEs
35B45 A priori estimates in context of PDEs
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76N15 Gas dynamics, general
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