Singular limits for the two-phase Stefan problem

TL;DR

This paper investigates the singular limits of a linearized inhomogeneous Stefan problem, analyzing how different combinations of surface tension and kinetic undercooling coefficients affect the convergence behavior.

Contribution

It establishes strong convergence results for various singular limits of the Stefan problem using uniform maximal regularity estimates, covering five different cases.

Findings

Strong convergence to singular limits proven for all cases

Uniform maximal regularity estimates are key to the analysis

Different coefficient limits lead to distinct types of singular behavior

Abstract

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 $\sigma \to \sigma_0$ and $\delta \to\delta_0$, where $\sigma,\sigma_0 \ge 0$ and $\delta,\delta_0 \ge 0$ 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.