Up-wind difference approximation and singularity formation for a slow erosion model

Coclite, Giuseppe Maria; Gargano, Francesco; Sciacca, Vincenzo

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 54 (2020) no. 2, pp. 465-492.

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We consider a model for a granular flow in the slow erosion limit introduced in [31]. We propose an up-wind numerical scheme for this problem and show that the approximate solutions generated by the scheme converge to the unique entropy solution. Numerical examples are also presented showing the reliability of the scheme. We study also the finite time singularity formation for the model with the singularity tracking method, and we characterize the singularities as shocks in the solution.

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