Published online by Cambridge University Press: 16 July 2009
We prove that in the Stefan problem with planar, cylindrical or spherical symmetry, with vanishing heat capacity and constant boundary temperature, no mushy region can appear, even in the presence of constant volumetric heat sources, if the initial data are consistent with the presence of just two pure phases. If the boundary temperature is not constant, a mushy region may or may not appear; we find some general conditions ensuring one case or the other and we give a specific example illustrating the appearance of a mushy region.