Convergence of the two-phase Stefan problem to the one-phase problem
Barbara E. E. Stoth · Quarterly of Applied Mathematics · 1997
We study the limit of the one-dimensional Stefan problem as the diffusivity coefficient of the solid phase approaches zero. We derive a weak formulation of the equilibrium condition for the resulting one-phase problem that allows jumps of the temperature across the interface. The weak formulation consists of a regularity condition that only enforces the usual equilibrium condition to hold from the liquid phase.