Geodesic
$L^1$ singular limit for relaxation and viscosity approximations of extended traffic flow models
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper considers the Cauchy problem for an extended traffic flow model with $$ |\rho(t,x)| \leq \sqrt {|\rho_0(x)|_1/(ct)} $$ derived from one of Lax's results and Diller's idea, the limit function $\rho(t,x)$ is shown to be a $L^1$-entropy week solution. A direct byproduct is that we can get the existence of $L^1$-entropy solutions for the Cauchy problem of the scalar conservation law with $L^1$-bounded initial data without any restriction on the growth exponent of the flux function provided that the flux function is strictly convex. Our result shows that, unlike the weak solutions of the incompressible fluid flow equations studied by DiPerna and Majda in [6], for convex scalar conservation laws with $L^1$-bounded initial data, the concentration phenomenon will never occur in its global entropy solutions.
Classification : 35B40, 35L65
Keywords: singular limit, traffic flow model, relaxation and viscosity approximation 
@article{EJDE_2003__2003__a199,
     author = {Klingenberg, Christian and Lu, Yunguang and Zhao, Huijiang},
     title = {$L^1$ singular limit for relaxation and viscosity approximations of extended traffic flow models},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a199/}
}
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%J Electronic Journal of Differential Equations
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Klingenberg, Christian; Lu, Yunguang; Zhao, Huijiang. $L^1$ singular limit for relaxation and viscosity approximations of extended traffic flow models. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a199/