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On non‐entropy solutions of scalar conservation laws for traffic flow
Author(s) -
Gasser I.
Publication year - 2003
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200310013
Subject(s) - conservation law , entropy (arrow of time) , scalar (mathematics) , statistical physics , microscopic traffic flow model , mathematics , mathematical economics , physics , mathematical analysis , statistics , thermodynamics , geometry , traffic generation model
We consider traffic flow models described by a scalar conservation law. For realistic equilibrium velocity distributions we show that the entropy condition gives solutions not corresponding to the reality. An alternative condition is formulated which seems to select reasonable solutions. Two examples, the “bump” and the “cluster”, are discussed.