- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:49
Rendiconti del Seminario Matematico della Università di Padova
Rend. Sem. Mat. Univ. Padova
RSMUP
0041-8994
2240-2926
General
10.4171/RSMUP
http://www.ems-ph.org/doi/10.4171/RSMUP
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2013)
131
2014
0
On the micro-macro limit in traffic flow
Rinaldo
Colombo
Università degli Studi di Brescia, BRESCIA, ITALY
E.
Rossi
Università di Milano-Bicocca, MILANO, ITALY
Macroscopic traffic models, microscopic traffic models, conservation laws
We investigate the relations between a macroscopic Lighthill-Whitham and Richards model and a microscopic follow-the-leader model for traffic flow. Solutions to the microscopic model are proved to tend to those to the macroscopic one in a sort of kinetic limit, i.e. as the number of individuals tends to $+ \infty$ while their total mass is constant. Based on this convergence result, we approximately compute the solutions to a conservation law by means of the integration of an ordinary differential system.
Partial differential equations
Operations research, mathematical programming
217
235
10.4171/RSMUP/131-13
http://www.ems-ph.org/doi/10.4171/RSMUP/131-13