A class of non-degenerate two-phase stefan problems in several space variables
Ricardo H. Nochetto · Communications in Partial Differential Equations · 1987
The singular parabolic equation with either Dirichlet or nonlinear Neumann boundary conditions is considered (u temperature, γ(u) enthalph). Under some qualitative assumptions upon the data it is shown that the mushy region is described by two Lipschitz-continuous functions and . When , hence mushy regions cannot appear spontaneously and u satisfies the non-degeneracy property:.