Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional case
Résumé
A multi-dimensional junction is the singular $d$-manifold obtained by gluying through their boundaries a finite number of copies of a half-hyperplane of $\mathbf{R}^{d+1}$. We show that the general theory developed by the authors (2013) for the network setting can be easily adapted to this multi-dimensional case. In particular, we prove that general 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.
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