Volume 54, Number 2, March-April 2020
|Page(s)||679 - 704|
|Published online||10 March 2020|
Well-posedness of a non-local model for material flow on conveyor belts
Inria Sophia Antipolis – Méditerranée, Université Côte d’Azur, Inria, CNRS, LJAD, 2004 Route des Lucioles – BP 93, 06902 Sophia Antipolis Cedex, France
2 Current affilliation: Università degli Studi di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via R. Cozzi 55, 20126 Milano, Italy
3 University of Mannheim, Department of Mathematics, 68131 Mannheim, Germany
* Corresponding author: email@example.com
Accepted: 26 August 2019
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.
Mathematics Subject Classification: 35L65 / 65M12
Key words: Non-local conservation laws / material flow / Roe scheme / Lax–Friedrichs scheme
© EDP Sciences, SMAI 2020
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