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 introduced in [P.-L. Lions and P. E. Souganidis, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 27 (2016), pp. 535–545], we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out.
A differential model for growing sandpiles on networks
Camilli, Fabio;
2018-01-01
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 introduced in [P.-L. Lions and P. E. Souganidis, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 27 (2016), pp. 535–545], we prove existence and uniqueness of the solution of the system and we discuss its numerical approximation. Some numerical experiments are carried out.File in questo prodotto:
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