We studied a one-dimensional free boundary problem arising in the polymer industry, which solution has an interesting asymptotic behavior when a convective boundary condition is imposed. We show the asymptotic behavior of the free boundary and of the concentration of the solvent in the domain, for large t. Exact estimates and numerical results are obtained.

In this paper, we consider a slab represented by the interval 0 < x < 1, at the initial temperature u0(x) > 0 and having a heat flux q(t) on the left face and a nonlinear condition on the right face x = 1. We consider the corresponding heat conduction problem and we assume that the phase-change temperature is 0ºC. We prove that certain conditions on the data are necessary and sufficient in order to obtain estimations of the occurrence of a phase-change in the material.