no. 1
Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 163-180.

We prove the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide L ∞ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the entropy condition through the doubling of variable technique. The limit model as the kernel support tends to infinity is also studied.

DOI : 10.1051/m2an/2017066
Classification : 35L65, 65M12
Mots clés : Non-local conservation laws, Lax-Friedrichs scheme
Chiarello, Felisia Angela 1 ; Goatin, Paola 1

1 
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     title = {Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {163--180},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {1},
     year = {2018},
     doi = {10.1051/m2an/2017066},
     zbl = {1395.35142},
     mrnumber = {3808157},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2017066/}
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Chiarello, Felisia Angela; Goatin, Paola. Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 1, pp. 163-180. doi : 10.1051/m2an/2017066. http://www.numdam.org/articles/10.1051/m2an/2017066/

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