| Abstract: |
| We present a many-particle approximation of Conservation Laws (CLs). The unique entropy solution to the IVP for a scalar CL was rigorously approximated in [1, 2] by a discrete density constructed from the follow-the-leader model. The IBVP for a scalar CL has been considered in [4]. The results in [1] have been extended in [3] to a $2\times2$ system of CLs. Finally, we present the extensions obtained in [5] for the one dimensional Hughes model for pedestrian flows. \
References\
[1] M.Di Francesco, M.D.Rosini, Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit. Archive for rational mechanics and analysis, 217(3):831-871, 2015\
[2] M.Di Francesco, S. Fagioli, M.D.Rosini, Deterministic particle approximation of scalar conservation laws, Bollettino dell`Unione Matematica Italiana 10:487-501, 2017\
[3] M. Francesco, S. Fagioli, M.D.Rosini, Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic. Mathematical Biosciences and Engineering, 14(1):127-141, 2017\
[4] M.Di Francesco, S. Fagioli, M.D.Rosini, G.Russo, Follow-the-leader approximations of macroscopic models for vehicular and pedestrian flows. Active Particles, Volume 1, Springer International Publishing, Cham, pp. 333-378, 2017\
[5] M.Di Francesco, S. Fagioli, M.D.Rosini, G.Russo, Deterministic particle approximation of the Hughes model in one space dimension. Kinetic and Related Models, 10(1):215-237, 2017 |
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