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Journal Articles SIAM Journal on Numerical Analysis Year : 2015

Nonlocal systems of conservation laws in several space dimensions

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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Dates and versions

hal-01016784 , version 1 (01-07-2014)

Identifiers

  • HAL Id : hal-01016784 , version 1

Cite

Aekta Aggarwal, Rinaldo M. Colombo, Paola Goatin. Nonlocal systems of conservation laws in several space dimensions. SIAM Journal on Numerical Analysis, 2015, 52 (2), pp.963-983. ⟨hal-01016784⟩
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