On existence of entropy solutions for 1D nonlocal conservation laws with space discontinuous flux

We prove the well-posedness of entropy weak solutions for a class of 1D space-discontinuous scalar conservation laws with non-local flux, describing traffic flow on roads with rough conditions. We approximate the problem through a Godunov-type numerical scheme and provide L^\infty and BV estimates for the approximate solutions. The limit model as the kernel support tends to zero is numerically investigated

Systems of conservation laws with discontinuous fluxes and applications to traffic

In this paper we study 2 × 2 systems of partial differential equations with discontinuous fluxes arising in vehicular traffic modeling. The main goal is to introduce an appropriate notion of solution. To this aim we consider physically reasonable microscopic follow-the-leader models. Macroscopic Riemann solvers are then obtained as many particle limits