A differential model for growing sandpiles on networks
This work provides a theoretical foundation for modeling granular flow on networks, but it is incremental as it extends existing Hamilton-Jacobi theory to a new application.
The authors develop a differential model for equilibrium configurations of granular material on networks, proving existence and uniqueness of solutions and demonstrating numerical approximations.
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.