On the analysis of a mathematical model for metal matrix composites manufacturing

We prove the existence and uniqueness theorems for a free boundary problem formulated as a mathematical model for metal matrix composites manufacturing. The process consists of the injection of a liquid metal through a rigid porous solid, accompanied by partial solidification and subsequent remelting. A technologically relevant qualitative property here investigated is a condition ensuring that solidification does not proceed to a point that the molten metal flow is stopped before the complete filling of the mould.