caa a22 4500 605515581 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s00205-015-0843-4 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0843-4 Rigorous Derivation of Nonlinear Scalar Conservation Laws from Follow-the-Leader Type Models via Many Particle Limit [Elektronische Daten] [M. Di Francesco, M.D. Rosini] We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly monotone velocity and nonnegative initial condition can be rigorously obtained as the large particle limit of a microscopic follow-the-leader type model, which is interpreted as the discrete Lagrangian approximation of the nonlinear scalar conservation law. More precisely, we prove that the empirical measure (respectively the discretised density) obtained from the follow-the-leader system converges in the 1-Wasserstein topology (respectively in $${\mathbf{L^{1}_{loc}}}$$ L loc 1 ) to the unique Kružkov entropy solution of the conservation law. The initial data are taken in $${\mathbf{L}^\infty}$$ L ∞ , nonnegative, and with compact support, hence we are able to handle densities with a vacuum. Our result holds for a reasonably general class of velocity maps (including all the relevant examples in the applications, for example in the Lighthill-Whitham-Richards model for traffic flow) with a possible degenerate slope near the vacuum state. The proof of the result is based on discrete $${\mathbf{BV}}$$ BV estimates and on a discrete version of the one-sided Oleinik-type condition. In particular, we prove that the regularizing effect $${\mathbf{L}^\infty \mapsto \mathbf{BV}}$$ L ∞ ↦ BV for nonlinear scalar conservation laws is intrinsic to the discrete model. Springer-Verlag Berlin Heidelberg, 2015 Di Francesco M. Department of Information Engineering, ComputerScience, and Mathematics, University of L'Aquila, Via Vetoio 1, Coppito, 67100, L'Aquila, Italy aut Rosini M.D. ICM, University of Warsaw, ul. Prosta 69, 00-838, Warsaw, Poland aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 831-871 0003-9527 217:3<831 2015 217 205 https://doi.org/10.1007/s00205-015-0843-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0843-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Di Francesco M. Department of Information Engineering, ComputerScience, and Mathematics, University of L'Aquila, Via Vetoio 1, Coppito, 67100, L'Aquila, Italy aut NATIONALLICENCE 700 1- Rosini M.D. ICM, University of Warsaw, ul. Prosta 69, 00-838, Warsaw, Poland aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/3(2015-09-01), 831-871 0003-9527 217:3<831 2015 217 205