A nonlinear two-phase Stefan problem with melting point gradient: a constructive approach

Abstract

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 pressure-dependent 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 numerical method. Numerical results are presented.