On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition
(i-5> 6x{0,t) = dx{l,t) = 0. (1.6) This problem is a model of the one-dimensional motion of the polytropic ideal gas with adiabatic ends which is put into a vacuum. (u,v,6), unknown functions, represent the specific volume, the velocity, the absolute temperature of the gas; (R, n,Cy ,k), given positive constants, stand for the gas constant, the coefficient of viscosity, the heat capacity at constant volume, and the coefficient of heat conduction, respectively. The condition (1.5) is called the stress-free condition. Kazhykhov showed the global existence of a unique solution to this problem in [2], He constructed the solution (u,v,6) in the Holder class Dt>o^7+" x H2r+a x H^+"} (0 < a < 1) provided (wo, vq, Go) belongs to Hl+a x H2+a x H2+a. (For the definition of the Holder spaces Hn+a etc., see [3].) We call this solution classical in this paper. More recently Okada [5] and Kawashima [1] showed the asymptotic behavior of the solution. The problem has a trivial solution