{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:35:24Z","timestamp":1787322924364,"version":"build-2736575974"},"reference-count":50,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>We introduce a new homogenized hyperbolic (multiclass) traffic flow model, which allows us to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.) and drivers. We discretize the starting Lagrangian system introduced below with a Godunov scheme, and we let the mesh size h in (x,t) go to 0: the typical length (of a vehicle) and time vanish. Therefore, the variables---here (w,a)---which describe the heterogeneity of the reactions of the different car-driver pairs in the traffic, develop large oscillations when $h\\rightarrow 0$. These (known) oscillations in (w,a) persist in time, and we describe the homogenized relations between velocity and density. We show that the velocity is the unique solution \"\u00e0 la Kruzkov\" of a scalar conservation law, with variable coefficients, discontinuous in x. Finally, we prove that the same macroscopic homogenized model is also the hydrodynamic limit of the corresponding multiclass Follow-the-Leader model.<\/jats:p>","DOI":"10.1137\/s0036141002411490","type":"journal-article","created":{"date-parts":[[2003,11,7]],"date-time":"2003-11-07T11:19:22Z","timestamp":1068203962000},"page":"949-973","source":"Crossref","is-referenced-by-count":50,"title":["A Multiclass Homogenized Hyperbolic Model of Traffic Flow"],"prefix":"10.1137","volume":"35","author":[{"given":"P.","family":"Bagnerini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"M.","family":"Rascle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,8,1]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139997332099"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139900380955"},{"key":"R3","first-page":"401","volume":"10","author":"Baiti Paolo","year":"1997","journal-title":"Differential Integral Equations"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1997.3308"},{"key":"R5","unstructured":"J. Ball, A version of the fundamental theorem for Young measures, Lecture Notes in Phys., Vol. 344, Springer, Berlin, 1989, 207\u201321591c:49021"},{"key":"R6","unstructured":"S. Benzoni\u2010Gavage and R. M. Colombo,\n                      An n\u2010Populations Model for Traffic Flow\n                      , preprint, http:\/\/www.umpa.ens\u2010lyon.fr\/\u02dcbenzonil\/ or http:\/\/dm.ing.unibs.it\/rinaldo\/, 2002;"},{"key":"R6","unstructured":"European J. Appl. 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Chanut,\n                      Vers une mod\u00e9lisation macroscopique d\u2019un \u00e9coulement bi\u2010fluide poids lourds et v\u00e9hicules l\u00e9gers\n                      , Ph.D. thesis, ENTPE, Vaulx en Velin, France, in preparation."},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160440105"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9364-1"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22019-1"},{"key":"R17","unstructured":"C. F. Daganzo,\n                      A Behavioral Theory of Multi\u2010lane Traffic Flow. 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Prigogine,\n                      Kinetic Theory of Vehicular Traffic\n                      , American Elsevier, New York, 1971."},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1998.3624"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1080\/03605309508821159"},{"issue":"123","key":"R27","first-page":"228","volume":"81","author":"Kru\u017ekov S.","year":"1970","journal-title":"Mat. Sb. (N.S.)"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8629-1"},{"key":"R29","unstructured":"P. L. Lions, G. Papanicolaou, and S. R. S. Varadhan,\n                      Homogenisation of Hamilton\u2010Jacobi Equations\n                      , manuscript."},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-6824-1"},{"key":"R31","first-page":"309","volume":"60","author":"Murat Fran\u00e7ois","year":"1981","journal-title":"J. Math. Pures Appl. 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