On the physical and the self-similar viscous approximation of a boundary Riemann problem

We deal with the viscous approximation of a system of conservation laws in one space dimension and we focus on initial-boundary value problems. It is known that, in general, different viscous approximation provide different limits because of boundary layer phenomena. We focus on Riemann-type data and we discuss a uniqueness criterion for distributional solutions which applies to both the non characteristic and the boundary characteristic case.