scholarly journals Well-posedness of the non-local conservation law by stochastic perturbation

2019 ◽  
Vol 162 (3-4) ◽  
pp. 367-387
Author(s):  
Christian Olivera
Keyword(s):  
Conservation Law ◽  
Stochastic Perturbation ◽  
Well Posedness ◽  
Local Conservation ◽  
Non Local ◽  
Local Conservation Law

scholarly journals GPU‐accelerated simulation of a non‐local conservation law

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Simone Göttlich ◽  
Jann Müller ◽  
Jennifer Weissen
Keyword(s):  
Conservation Law ◽  
Local Conservation ◽  
Accelerated Simulation ◽  
Non Local ◽  
Local Conservation Law

scholarly journals Well-posedness of a conservation law with non-local flux arising in traffic flow modeling

2015 ◽  
Vol 132 (2) ◽  
pp. 217-241 ◽  
Author(s):  
Sebastien Blandin ◽  
Paola Goatin
Keyword(s):  
Traffic Flow ◽  
Conservation Law ◽  
Well Posedness ◽  
Flow Modeling ◽  
Non Local

scholarly journals A non-local traffic flow model for 1-to-1 junctions

2019 ◽  
Vol 31 (6) ◽  
pp. 1029-1049
Author(s):  
F. A. CHIARELLO ◽  
J. FRIEDRICH ◽  
P. GOATIN ◽  
S. GÖTTLICH ◽  
O. KOLB
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Approximate Solutions ◽  
Well Posedness ◽  
Local Conservation ◽  
Flow Modelling ◽  
Vehicle Density ◽  
Proposed Model ◽  
Non Local ◽  
Traffic Flow Modelling

We present a model for a class of non-local conservation laws arising in traffic flow modelling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions, and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax–Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.

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