Existence and uniqueness of a classical solution for a mathematical model describing the isobaric crystallization of a polymer

In this paper a global existence and uniqueness result is presented for the classical solution of a free boundary problem for a system of partial differential equations (p.d.e.s) with non-local boundary conditions describing the crystallization process of a cylindrical sample of polymer under prescribed pressure. The system of equations is discussed in [16] as the model for coupled cooling and shrinking of a sample of molten polymer under a given constant pressure. The velocity field generated by the thermal and chemical contraction enters the model only through its divergence. Such an approximation is discussed on the basis of a qualitative analysis.