Singular limits for the two-phase Stefan problem

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.

27 pages. To appear

References in corpus (2)

• Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension
• On thermodynamically consistent Stefan problems with variable surface energy

Cited by in corpus (1)

• On the flow of non-axisymmetric perturbations of cylinders via surface diffusion