  We provide a detailed analysis of the boundary layers for mixed
hyperbolic-parabolic systems in one space dimension and small amplitude
regimes. As an application of our results, we describe the solution of the
so-called boundary Riemann problem recovered as the zero viscosity limit of the
physical viscous approximation. In particular, we tackle the so called doubly
characteristic case, which is considerably more demanding from the technical
viewpoint and occurs when the boundary is characteristic for both the mixed
hyperbolic-parabolic system and for the hyperbolic system obtained by
neglecting the second order terms. Our analysis applies in particular to the
compressible Navier-Stokes and MHD equations in Eulerian coordinates, with both
positive and null conductivity. In these cases, the doubly characteristic case
occurs when the velocity is close to 0. The analysis extends to
non-conservative systems.
