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Weak formulation of boundary conditions for scalar conservation laws: an application to highway traffic modelling
Author(s) -
S. Strub Issam,
M. Bayen Alexandre
Publication year - 2006
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.1099
Subject(s) - conservation law , uniqueness , godunov's scheme , scalar (mathematics) , bounded function , context (archaeology) , boundary (topology) , convergence (economics) , weak solution , mathematics , weak formulation , boundary value problem , mathematical optimization , numerical analysis , mathematical analysis , geometry , economics , paleontology , biology , economic growth
This article proves the existence and uniqueness of a weak solution to a scalar conservation law on a bounded domain. A weak formulation of the boundary conditions is needed for the problem to be well posed. The existence of the solution results from the convergence of the Godunov scheme. This weak formulation is written explicitly in the context of a strictly concave flux function (relevant for highway traffic). The numerical scheme is then applied to a highway scenario with data from highway Interstate‐80 obtained from the Berkeley Highway Laboratory. Finally, the existence of a minimiser of travel time is obtained, with the corresponding optimal boundary control. Copyright © 2006 John Wiley & Sons, Ltd.