Existence of analytic solutions for the classical Stefan problem

Existence of Analytic Solutions for the Classical Stefan Problem

We prove that under mild regularity assumptions on the initial data the two-phase classical Stefan problem admits a (unique) solution that is analytic in space and time.

Analytic Solutions for a Stefan Problem with Gibbs-thomson Correction

Classical two - phase Stefan problem for spheres

The classical Stefan problem for freezing (or melting) a sphere is usually treated by assuming that the sphere is initially at the fusion temperature, so that heat flows in one phase only. Even in this idealized case there is no (known) exact solution, and the only way to obtain meaningful results is through numerical or approximate means. In this study, the full two-phase problem is considered...

Existence of weak solutions for the Stefan problem with anisotropic Gibbs-Thomson law

The Stefan problem with Gibbs-Thomson law describes solidification phenomena for pure substances. In applications the surface energy is anisotropic leading to an anisotropic Gibbs-Thomson law. We show the existence of weak solutions to the Stefan problem with anisotropic Gibbs-Thomson law using an implicit time discretization, and variational methods in an anisotropic BV setting. Our main resul...

Vanishing Specific Heat for the Classical Solutions of a Multidimensional Stefan Problem with Kinetic Condition

In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat e goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space in which we can get the existence and...