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Nonlocal systems of conservation laws in several space dimensions

Aekta Aggarwal 1 Rinaldo M. Colombo 2 Paola Goatin 3
1 OPALE - Optimization and control, numerical algorithms and integration of complex multidiscipline systems governed by PDE
CRISAM - Inria Sophia Antipolis - Méditerranée , JAD - Laboratoire Jean Alexandre Dieudonné : UMR6621
3 Acumes - Analysis and Control of Unsteady Models for Engineering Sciences
CRISAM - Inria Sophia Antipolis - Méditerranée
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 $\delta$, the nonlocal problem converges to its non-nonlocal analogue.
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Aekta Aggarwal, Rinaldo M. Colombo, Paola Goatin. Nonlocal systems of conservation laws in several space dimensions. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2015, 52 (2), pp.963-983. ⟨hal-01016784⟩

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