  We complete the Solomon-Wilson-Alexiades's mushy zone model (Letters Heat
Mass Transfer, 9 (1982), 319-324) for the one-phase Lam\'e-Clapeyron-Stefan
problem. We obtain explicit solutions when a convective or heat flux boundary
condition is imposed on the fixed face for a semi-infinite material. We also
obtain the necessary and sufficient condition on data in order to get these
explicit solutions. Moreover, when these conditions are satisfied the two
problems are equivalents to the same problem with a temperature boundary
condition on the fixed face and therefore an inequality for the coefficient
which characterized one of the two free interfaces is also obtained.
