Quasi-convex Hamilton-Jacobi equations posed on junctions: the multi-dimensional caseReport as inadecuate




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

Abstract : 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.

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





Author: Cyril Imbert - R Monneau -

Source: https://hal.archives-ouvertes.fr/



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