An approximation scheme for a Hamilton-Jacobi equation defined on a network

Fabio Camilli (1) , Adriano Festa , Dirk Schieborn

1 MeMoMat - Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate

An important problem in graph theory is to detect the shortest paths connecting the vertices of a graph to a prescribed target vertex. Here we study a generalization of the previous problem: finding the shortest path connecting any point of a graph (and not only a vertex) to the target. Our approach is based on the study of Eikonal equations and the corresponding theory of viscosity solutions on topological graphs.

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Fabio Camilli, Adriano Festa, Dirk Schieborn. An approximation scheme for a Hamilton-Jacobi equation defined on a network. Applied Numerical Mathematics, 2013, 73, pp.33-47. ⟨10.1016/j.apnum.2013.05.003⟩. ⟨hal-00724768⟩