Nonlocal Systems of Conservation Laws in Several Space Dimensions

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion de documents scientifiques de niveau recherche, publiés ou non, ´ emanant desétablissements d'enseignement et de recherche français oú etrangers, des laboratoires publics ou privés. Abstract. We present a Lax–Friedrichs type algorithm to numerically integrate a class of nonlocal and nonlinear systems of conservation laws in several space dimensions. The convergence of the approximate solutions is proved, also providing the existence of solution in a slightly more general setting than in other results in the current literature. An application to a crowd dynamics model is considered. This numerical algorithm is then used to test the conjecture that as the convolution kernels converge to a Dirac δ, the nonlocal problem converges to its non-nonlocal analogue.