A Stefan problem on an evolving surface

A Stefan problem on an evolving surface.

We formulate a Stefan problem on an evolving hypersurface and study the well posedness of weak solutions given L(1) data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then, we consider the existence of solutions for L(∞) data; this is done by regularization of the nonlinearity. The regulari...

1 0 Ju l 2 01 5 A Stefan problem on an evolving surface

We formulate a Stefan problem on an evolving hypersurface and study the wellposedness of weak solutions given L1 data. To do this, we first develop function spaces and results to handle equations on evolving surfaces in order to give a natural treatment of the problem. Then we consider the existence of solutions for L∞ data; this is done by regularisation of the nonlinearity. The regularised pr...

On the Stefan Problem with Surface Tension

1. Introduction The classical Stefan problem is a model for phase transitions in solid-liquid systems and accounts for heat diiusion and exchange of latent heat in a homogeneous medium. The strong formulation of this model corresponds to a moving boundary problem involving a parabolic diiusion equation for each phase and a transmission condition prescribed at the interface separating the phases...

An Inverse Stefan Problem

The Stefan Problem with Small Surface Tension

The Stefan problem with small surface tension e is considered. Assuming that the classical Stefan problem (with s = 0) has a smooth free boundary T, we denote the temperature of the solution by 60 and consider an approximate solution 60 + su for the case where e ^ 0, e small. We first establish the existence and uniqueness of u , and then investigate the effect of u on the free boundary T. It i...