Nonlocal reaction traffic flow model with on-off ramps (Q2138388)

The authors introduce a nonlocal balance law to model vehicular traffic flow including on- and off-ramps. Three models are presented and they are called Model 0, Model 1 and Model 2. The existence for Model 1 and Model 2 is proved. The problem is approximated using an upwind-type numerical scheme, providing a maximum principle, and \(\mathbf{L}^{\infty}\) and \(\mathbf{BV}\) estimates for the sequence of the approximate solutions. A discrete entropy inequality and well-posedness of the considered class of scalar balance laws are also shown. The numerical tests show that Model 0 does not satisfy a maximum principle. A limit model as the kernel support tends to zero is numerically investigated.