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Convergence of the follow-the-leader scheme for scalar conservation laws with space dependent flux

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  • This paper deals with the derivation of entropy solutions to Cauchy problems for a class of scalar conservation laws with space-density depending fluxes from systems of deterministic particles of follow-the-leader type. We consider fluxes which are product of a function of the density $ v(\rho) $ and a function of the space variable $ \phi(x) $. We cover four distinct cases in terms of the sign of $ \phi $, including cases in which the latter is not constant. The convergence result relies on a local maximum principle and on a uniform $ BV $ estimate for the approximating density.

    Mathematics Subject Classification: Primary: 35L65, 35F25; Secondary: 82C22, 90B20.


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