Introduction of a non constant viscosity on an extrusion process: improvements

The aim of this paper is to improve previous works about an extrusion process which is expressed by two systems of conservation laws (with source terms) coupled by a moving interface whose relation is derived from the conservation of momentum. Previous articles have shown the well-posedness and the stability of the linearized system and performed a PI control of the system via an Internal Model Boundary Control structure; for which the parameters have been tuned using the perturbation theory of C0-semigroup. Those works have been done with simplifying hypothesis like constant viscosity and melt density. Here, the same reasoning is done, taken this time a viscosity and a melt density as functions of the temperature. Some simulations are done with a constant melt density and a viscosity function of the temperature.