2017/02/28 by Simone Cacace, Cacace, Simone, Fabio Camilli +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Numerical Analysis (math.NA) #Slime Mold and Myxomycetes Research
paper · doi:10.48550/arxiv.1702.08697
openalex publication_date 2017/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.