Stability for the one-dimensional equation of a viscous heat-conducting gas with a variable domain

We consider the equation of a one-dimensional viscous heat-conducting compr essible gas in the variable domain with the appropriate boundary conditions . We study the large-time behaviour of the solution in the particular case where the displacement of the variable boundary is given by L(t) = L-0(1 at)(alpha) with 0 < <alpha> < 1, where a is a positive constant and L-0 is the initial amplitude of our domain.