Well posedness of the model of an extruder in infinite dimension

The topic of this paper is to present and analyse a physical model of the extrusion process which is expressed two systems of conservation laws (with source terms) coupled by a moving interface whose relation is derived from the conservation of momentum. After a change of variables on the spatial variables is performed in order to transform the time-varying spatial domain in fixed one, the linearisation of the model around an equilibrium profile is given, the well-posedness in the sense of the existence of a C₀-semigroup of those the coupled systems is proven.