In this talk, we study the existence and stability of steady solutions of viscous conservations laws and the compressible Navier Stokes equations with noncharacteristic boundary conditions. Depending on the boundary conditions, a shock or a boundary layer can appear. On a bounded interval, different phenomena can occur : a shock can concentrate close to the boundary or a boundary layer can appear on both sides (double boundary layer). First, we will perform numerical simulations to show these phenomena. Then, we will prove existence and uniqueness of steady solutions. Finally we will talk about the stability of these steady solutions in two different cases : small viscosity and strong viscosity.