Well-posedness of the extrusion model described by coupled hyperbolic systems with a free boundary

TL;DR

This paper proves the existence, uniqueness, and regularity of solutions for a mathematical model of the extrusion process described by coupled hyperbolic systems with a free boundary.

Contribution

It establishes well-posedness for a complex extrusion model using coordinate transformation and fixed point methods, advancing mathematical understanding of free boundary problems.

Findings

Existence of weak solutions confirmed.

Uniqueness of solutions established.

Regularity properties demonstrated.

Abstract

In this paper, we consider the well-posedness of the Cauchy problem for a physical model of the extrusion process, which is described by two systems of conservation laws with a free boundary. By suitable change of coordinates and fixed point argument, we obtain the existence, uniqueness and regularity of the weak solution to this Cauchy problem.