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

Elena Rossi (1) , Jennifer Kötz (2) , Paola Goatin (1) , Simone Göttlich (2)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
2 Department of Mathematics and Computer Science [Mannheim]

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.

Mots clés: non-local conservation laws; Roe scheme; Lax-Friedrichs scheme; material flow

Domaines: Equations aux dérivées partielles [math.AP]

Elena Rossi, Jennifer Kötz, Paola Goatin, Simone Göttlich. Well-posedness of a non-local model for material flow on conveyor belts. ESAIM: Mathematical Modelling and Numerical Analysis, 2020, 54 (2), pp.679-704. ⟨10.1051/m2an/2019062⟩. ⟨hal-02022654⟩