  In this paper, we are concerned with the one-dimensional initial boundary
value problem for isentropic gas dynamics.
  Through the contribution of great researchers such as Lax, P. D., Glimm, J.,
DiPerna, R. J. and Liu, T. P., the decay theory of solutions was established.
They treated with the Cauchy problem and the corresponding initial data have
the small total variation. On the other hand, the decay for initial data with
large oscillation has been open for half a century. In addition, due to the
reflection of shock waves at the boundaries, little is known for the decay of
the boundary value problem on a bounded interval.
  Our goal is to prove the existence of a global attractor, which yields a
decay of solutions for large data. To construct approximate solutions, we
introduce a modified Godunov scheme.
