The known pseudo-concentration model is a generalization of the classical model of two immiscible fluids when the interface between the two fluids is not a sufficiently regular curve. Besides, it provides efficient and robust numerical methods. The aim of this article is to prove existence of solutions to a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. Numerical methods and numerical simulations with comparison with

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... ntal results have been presented in [6]; [7]. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a renormalized solution to the mathematical model, and an analysis of time stability is carried out illustrating that the proposed model is suitable for describing the polymer state.