We will talk about the initial boundary value problem for barotropic Navier-Stokes system in 1D half space, when we impose one of the three boundary conditions : impermeable, inflow and outflow at the origin, together with a constant state at far-field. We are interested in the case where the two constant states at the origin and the far-field are connected by a Hugoniot curve possibly together with rarefaction curve and boundary layer curve. In this talk, we will present the long-time behavior towards the following cases:

(i) Single shock for the Impermeable problem or Outflow problem;

 (ii) Superposition of the boundary layer solution, the 1-rarefaction wave, and the viscous 2-shock waves for the Inflow problem.