in this paper we consider a nonlinear two-phase stefan problem in one-dimensional space. the problem is mapped into a nonlinear volterra integral equation for the free boundary.

In this paper we consider a nonlinear two-phase Stefan problem in one-dimensional space. The problem is mapped into a nonlinear Volterra integral equation for the free boundary.

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...