Paper detail

Singular limits for the two-phase Stefan problem

We prove strong convergence to singular limits for a linearized fully inhomogeneous Stefan problem subject to surface tension and kinetic undercooling effects. Different combinations of $σ\to σ_0$ and $δ\toδ_0$, where $σ,σ_0 \ge 0$ and $δ,δ_0 \ge 0$ denote surface tension and kinetic undercooling coefficients respectively, altogether lead to five different types of singular limits. Their strong convergence is based on uniform maximal regularity estimates.