For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraphers equation). Existence and uniqueness of the free boundary is shown, and the connection to th...

A model for species diffusion is presented, with evaporation at a moving free boundary. The resulting problem resembles a one-phase Stefan problem with superheating, but the usual Stefan condition at the moving boundary is replaced by a version which, in the classical setting, would violate conservation of energy. In the fast evaporation limit, however, the problem reduces to a classical nonlin...

Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

We develop a high-order energy method to prove asymptotic stability of flat steady surfaces for the Stefan problem with surface tension also known as the Stefan problem with Gibbs-Thomson correction.

In this present study, volume of fluid method in OpenFOAM open source CFD package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. This model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. Both phases (liquid-va...

We investigate the interface dynamics in Laplacian growth model, using the conformal mapping technique. Starting from the governing equation obtained by B.Shraiman and D.Bensimon, we derive intergro-differential evolution equation of interphase dynamics. It is shown that such representation of the conformal mapping technique is convenient for computer simulations of the quasi-stationary Stefan ...

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...

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...