When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires ...

We consider a one-dimensional two-phase Stefan problem, modeling a layer of solid material floating on liquid. The model includes internal heat sources, variable total mass (resulting e.g. from sedimentation or erosion), and a pressuredependent melting point. The problem is reduced to a set of nonlinear integral equations, which provides the basis for an existence and uniqueness proof and a new...

We consider the Stefan problem, firstly with regular data and secondly irregular data. In both cases is given a proof for convergence of an approximation obtained by regularising problem. These proofs are based on weak formulations compactness results in some Sobolev spaces negative exponents.