Well-posedness and exact controllability of the mass balance equations for an extrusion process

TL;DR

This paper establishes the well-posedness and exact controllability of a coupled hyperbolic PDE and nonlinear ODE model describing mass balance in a food extrusion process, ensuring precise control of the system.

Contribution

It introduces a novel analytical approach combining coordinate change and fixed point methods to prove controllability of the coupled PDE-ODE system.

Findings

Existence and uniqueness of solutions are proven.

The coupled system is shown to be exactly controllable.

Regularity of solutions is established.

Abstract

In this paper, we study the well-posedness and exact controllability of a physical model for a food extrusion process in the isothermal case. The model expresses the mass balance in the extruder chamber and consists of a hyperbolic Partial Differential Equation (PDE) and a nonlinear Ordinary Differential Equation (ODE) whose dynamics describes the evolution of a moving interface. By suitable change of coordinates and fixed point arguments, we prove the existence, uniqueness and regularity of the solution, and finally the exact controllability of the coupled system.