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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2018

A Differential Model for Growing Sandpiles on Networks

Résumé

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.

Dates et versions

hal-04271073 , version 1 (05-11-2023)

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Simone Cacace, Fabio Camilli, Lucilla Corrias. A Differential Model for Growing Sandpiles on Networks. SIAM Journal on Mathematical Analysis, 2018, 50 (3), pp.2509-2535. ⟨10.1137/17M113143X⟩. ⟨hal-04271073⟩
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