scholarly journals Global entropy weak solutions for general non-local traffic flow models with anisotropic kernel

2018 ◽  
Vol 52 (1) ◽  
pp. 163-180 ◽  
Author(s):  
Felisia Angela Chiarello ◽  
Paola Goatin
Keyword(s):  
Weak Solutions ◽  
Approximate Solutions ◽  
Traffic Modeling ◽  
Scalar Conservation Laws ◽  
Flow Models ◽  
Limit Model ◽  
Traffic Flow Models ◽  
Non Local ◽  
Scalar Conservation ◽  
Anisotropic Kernel

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.

MECHANISMS FOR ERROR PROPAGATION AND CANCELLATION IN GLIMM'S SCHEME WITHOUT RAREFACTIONS

2007 ◽  
Vol 04 (03) ◽  
pp. 501-531 ◽  
Author(s):  
M. LAFOREST
Keyword(s):  
Error Propagation ◽  
Method Of Characteristics ◽  
Approximate Solutions ◽  
Posteriori Error ◽  
Scalar Conservation Laws ◽  
Wave Interactions ◽  
Single Wave ◽  
A Posteriori Error ◽  
Scalar Conservation ◽  
Norm Of The Error

We derive an a posteriori error bound for Glimm's approximate solutions to convex scalar conservation laws containing only shock waves. Using Liu's wave-tracing method, we show that the L1 norm of the error is bounded by a sum of residuals containing independent contributions from each wave in the approximate solution. We introduce a framework, similar to the method of characteristics, for the analysis of the local errors generated by wave interactions. The analysis allows for explicit cancellation among the errors created by a single wave and for error propagation along discontinuities.

scholarly journals On a quadratic functional for scalar conservation laws

2014 ◽  
Vol 11 (02) ◽  
pp. 355-435 ◽  
Author(s):  
Stefano Bianchini ◽  
Stefano Modena
Keyword(s):  
Convergence Rate ◽  
Conservation Laws ◽  
Natural Extension ◽  
Approximate Solutions ◽  
Quadratic Functional ◽  
Scalar Conservation Laws ◽  
Nonlinear Case ◽  
Glimm Scheme ◽  
Quadratic Interaction ◽  
Scalar Conservation

We prove a quadratic interaction estimate for approximate solutions to scalar conservation laws obtained by the wavefront tracking approximation or the Glimm scheme. This quadratic estimate has been used in the literature to prove the convergence rate of the Glimm scheme. The proof is based on the introduction of a quadratic functional 𝔔(t), decreasing at every interaction, and such that its total variation in time is bounded. Differently from other interaction potentials present in the literature, the form of this functional is the natural extension of the original Glimm functional, and coincides with it in the genuinely nonlinear case.

scholarly journals Non-local multi-class traffic flow models

2019 ◽  
Vol 14 (2) ◽  
pp. 371-387 ◽  
Author(s):  
Felisia Angela Chiarello ◽  
◽  
Paola Goatin
Keyword(s):  
Traffic Flow ◽  
Flow Models ◽  
Traffic Flow Models ◽  
Non Local
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