# A differential model for growing sandpiles on networks

## TL;DR

This paper models the equilibrium of granular material on networks using a differential system of Monge-Kantorovich type, establishing existence, uniqueness, and numerical methods for solutions.

## Contribution

It introduces a differential model for sandpiles on networks and proves well-posedness using viscosity solutions, with numerical approximation and experiments.

## Key findings

- Existence and uniqueness of solutions are proven.
- Numerical schemes for the model are developed.
- Numerical experiments validate the approach.

## Abstract

We consider a system of differential equations of Monge-Kantorovich type which describes the equilibrium configurations of granular material poured by a constant source on a network. Relying on the definition of viscosity solution for Hamilton-Jacobi equations on networks, recently introduced by P.-L. Lions and P. E. Souganidis, we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out.