1. A differential model for growing sandpiles on networks
- Author
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Lucilla Corrias, Fabio Camilli, Simone Cacace, Cacace, S., Camilli, F., and Corrias, L.
- Subjects
Mathematics::Analysis of PDEs ,Mathematics::Optimization and Control ,Type (model theory) ,Monge–Kantorovich system ,Granular material ,01 natural sciences ,Mathematics - Analysis of PDEs ,Granular matter ,0103 physical sciences ,FOS: Mathematics ,Mathematics - Numerical Analysis ,0101 mathematics ,010306 general physics ,Mathematics ,Applied Mathematics ,010102 general mathematics ,Mathematical analysis ,Numerical Analysis (math.NA) ,Networks ,Viscosity solutions ,Analysis ,Computational Mathematics ,System of differential equations ,Constant (mathematics) ,Differential (mathematics) ,Analysis of PDEs (math.AP) - 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.
- Published
- 2018
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