Preprint 2021-09
Felisia A. Chiarello, Luis M. Villada:
On existence of entropy solutions for 1D nonlocal conservation laws with space-discontinous flux
Abstract:
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 $\mathbf{L}^\infty$ and $\mathbf{BV}$ estimates for the approximate solutions. The limit model as the kernel support tends to zero is numerically investigated.
This preprint gave rise to the following definitive publication(s):
Felisia A. CHIARELLO, Harold D. CONTRERAS, Luis M. VILLADA: Existence of entropy weak solutions for 1D non-local traffic models with space-discontinous flux. Journal of Engineering Mathematics, vol. 141, no. 9, (2023).