# Well-posedness of a non-local model for material flow on conveyor belts

## TL;DR

This paper investigates finite volume schemes for a non-local two-dimensional material flow model, proving convergence, stability, and comparing Roe-type and Lax-Friedrichs discretizations through numerical analysis.

## Contribution

It introduces a convergence proof for finite volume schemes applied to a non-local flow model, including a comparison of Roe and Lax-Friedrichs methods and establishing solution uniqueness.

## Key findings

- Roe scheme offers benefits over Lax-Friedrichs in numerical simulations.
- Convergence of approximate solutions is proven despite flux discontinuities.
- Solution depends continuously on initial data, ensuring uniqueness.

## Abstract

In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax-Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initial datum, ensuring the uniqueness of the solution.