Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case

Cyril Imbert (1) , R Monneau (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

A \emph{multi-dimensional junction} is the singular $(d+1)$-manifold obtained by gluying through their boundaries a finite number of copies of the half-space $\R^{d+1}_+$. We show that the general theory developed by the authors (2013) for the network setting can be adapted to this multi-dimensional case. In particular, we prove that general quasi-convex junction conditions reduce to flux-limited ones and that uniqueness holds true when flux limiters are quasi-convex and continuous. The proof of the comparison principle relies on the construction of a (multi-dimensional) vertex test function.

Mots clés: Quasi-convex Hamilton-Jacobi equations; multli-dimensional junctions; flux-limited solutions; flux limiters; comparison principle; multi-dimensional vertex test function; discontinuous Hamiltonians

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, R Monneau. Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case. 2016. ⟨hal-01073954v2⟩