Publicación: EXISTENCE OF ENTROPY WEAK SOLUTIONS FOR 1D NON-LOCAL TRAFFIC MODELS WITH SPACE-DISCONTINUOUS FLUX
Fecha
2023
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JOURNAL OF ENGINEERING MATHEMATICS
Resumen
WE STUDY A 1D SCALAR CONSERVATION LAW WHOSE NON-LOCAL FLUX HAS A SINGLE SPATIAL DISCONTINUITY. THIS MODEL IS INTENDED TO DESCRIBE TRAFFIC FLOW ON A ROAD WITH ROUGH CONDITIONS. WE APPROXIMATE THE PROBLEM THROUGH AN UPWIND-TYPE NUMERICAL SCHEME AND PROVIDE COMPACTNESS ESTIMATES FOR THE SEQUENCE OF APPROXIMATE SOLUTIONS. THEN, WE PROVE THE EXISTENCE AND THE UNIQUENESS OF ENTROPY WEAK SOLUTIONS. NUMERICAL SIMULATIONS CORROBORATE THE THEORETICAL RESULTS AND THE LIMIT MODEL AS THE KERNEL SUPPORT
TENDS TO ZERO IS NUMERICALLY INVESTIGATED.
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Numerical scheme · Traffic models, Non-local problem, Discontinuous flux, Conservation laws
