{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T04:23:49Z","timestamp":1772771029507,"version":"3.50.1"},"reference-count":23,"publisher":"EDP Sciences","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ESAIM: M2AN"],"published-print":{"date-parts":[[2015,1]]},"DOI":"10.1051\/m2an\/2014023","type":"journal-article","created":{"date-parts":[[2014,5,19]],"date-time":"2014-05-19T16:52:52Z","timestamp":1400518372000},"page":"19-37","source":"Crossref","is-referenced-by-count":60,"title":["On the Numerical Integration of Scalar Nonlocal Conservation Laws"],"prefix":"10.1051","volume":"49","author":[{"given":"Paulo","family":"Amorim","sequence":"first","affiliation":[]},{"given":"Rinaldo M.","family":"Colombo","sequence":"additional","affiliation":[]},{"given":"Andreia","family":"Teixeira","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2015,1,12]]},"reference":[{"key":"R1","unstructured":"Berres S., B\u00fcrger R., Karlsen K.H. and Tory E.M., Strongly degenerate parabolic-hyperbolic systems modeling polydisperse sedimentation with compression.SIAM J. Appl. Math.64(2003) 41\u201380."},{"key":"R2","doi-asserted-by":"crossref","unstructured":"Betancourt F., B\u00fcrger R., Karlsen K.H. and Tory E.M., On nonlocal conservation laws modelling sedimentation.Nonlinearity24(2011) 855\u2013885.","DOI":"10.1088\/0951-7715\/24\/3\/008"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"A. Bressan, Hyperbolic systems of conservation laws. The one-dimensional Cauchy problem, vol. 20 ofOxford Lect. Ser. Math. Applications. Oxford University Press, Oxford (2000).","DOI":"10.1093\/oso\/9780198507000.001.0001"},{"key":"R4","unstructured":"Caetano F., The linearization of a boundary value problem for a scalar conservation law.Commun. Math. Sci.6(2008) 651\u2013667."},{"key":"R5","doi-asserted-by":"crossref","unstructured":"Carrillo J.A., Colombo R.M., Gwiazda P. and Ulikowska A., Structured populations, cell growth and measure valued balance laws.J. Differ. Eqs.252(2012) 3245\u20133277.","DOI":"10.1016\/j.jde.2011.11.003"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"Colombo R.M., Garavello M. and L\u00e9cureux-Mercier M., A class of nonlocal models for pedestrian traffic.Math. Models Methods Appl. Sci.22(2012) 1150023, 34.","DOI":"10.1142\/S0218202511500230"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"Colombo R.M., Herty M. and Mercier M., Control of the continuity equation with a non local flow.ESAIM: COCV17(2011) 353\u2013379.","DOI":"10.1051\/cocv\/2010007"},{"key":"R8","unstructured":"Colombo R.M. and L\u00e9cureux-Mercier M., Nonlocal Crowd Dynamics Models for Several Populations.Acta Math. Sci. Ser. B Engl. Ed.32(2012) 177\u2013196."},{"key":"R9","unstructured":"Colombo R.M., Mercier M. and Rosini M.D., Stability and total variation estimates on general scalar balance laws.Commun. Math. Sci.7(2009) 37\u201365."},{"key":"R10","doi-asserted-by":"crossref","unstructured":"G. Crippa and M. L\u00e9cureux-Mercier, Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow.Nonlinear Differ. Eqs. Appl. NoDEA(2012) 1\u201315.","DOI":"10.1007\/s00030-012-0164-3"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"C.M. Dafermos, Hyperbolic conservation laws in continuum physics, vol. 325 ofGrundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 3rd edition (2010).","DOI":"10.1007\/978-3-642-04048-1"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"Eftimie R., Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review.J. Math. Biol.65(2012) 35\u201375.","DOI":"10.1007\/s00285-011-0452-2"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"Friedman A., Conservation laws in mathematical biology.Discrete Contin. Dyn. Syst.32(2012) 3081\u20133097.","DOI":"10.3934\/dcds.2012.32.3081"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"Gosse L. and James F.. Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients.Math. Comput.69987\u20131015, 2000.","DOI":"10.1090\/S0025-5718-00-01185-6"},{"key":"R15","unstructured":"Gwiazda P., Lorenz T. and Marciniak-Czochra A., A nonlinear structured population model: Lipschitz continuity of measure-valued solutions with respect to model ingredients.J. Differ. Eqs.248(2010) 2703\u20132735."},{"key":"R16","unstructured":"S. Gttlich, S. Hoher, P. Schindler, V. Schleper and A. Verl, Modeling, simulation and validation of material flow on conveyor belts. Prepint Reihe des Stuttgart Research Center for Simulation Technology, 746 (2013)."},{"key":"R17","doi-asserted-by":"crossref","unstructured":"Karlsen K.H. and Risebro N.H., Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients.ESAIM: M2AN35(2001) 239\u2013269.","DOI":"10.1051\/m2an:2001114"},{"key":"R18","unstructured":"Kru\u017ehkov S.N., First order quasilinear equations with several independent variables.Mat. Sb. (N.S.)81(1970) (123) 228\u2013255."},{"key":"R19","doi-asserted-by":"crossref","unstructured":"R.J. LeVeque, Finite volume methods for hyperbolic problems.Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge (2002).","DOI":"10.1017\/CBO9780511791253"},{"key":"R20","unstructured":"Lighthill M.J. and Whitham G.B., On kinematic waves. II. A theory of traffic flow on long crowded roads.Proc. Roy. Soc. London Ser. A.229(1955) 317\u2013345."},{"key":"R21","doi-asserted-by":"crossref","unstructured":"Nieto J., Poupaud F. and Soler J., High-field limit for the Vlasov-Poisson-Fokker-Planck system.Arch. Ration. Mech. Anal.158(2001) 29\u201359.","DOI":"10.1007\/s002050100139"},{"key":"R22","doi-asserted-by":"crossref","unstructured":"Piccoli B. and Tosin A., Time-evolving measures and macroscopic modeling of pedestrian flow.Arch. Ration. Mech. Anal.199(2011) 707\u2013738.","DOI":"10.1007\/s00205-010-0366-y"},{"key":"R23","unstructured":"Richards P.I., Shock waves on the highway.Oper. Res.4(1956) 42\u201351."}],"container-title":["ESAIM: Mathematical Modelling and Numerical Analysis"],"original-title":[],"link":[{"URL":"http:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2014023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,26]],"date-time":"2024-05-26T19:33:07Z","timestamp":1716751987000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.esaim-m2an.org\/10.1051\/m2an\/2014023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1]]},"references-count":23,"journal-issue":{"issue":"1"},"alternative-id":["m2an140023"],"URL":"https:\/\/doi.org\/10.1051\/m2an\/2014023","relation":{},"ISSN":["0764-583X","1290-3841"],"issn-type":[{"value":"0764-583X","type":"print"},{"value":"1290-3841","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1]]}}}