Section: New Results

Non-local conservation laws

Participants : Felisia Angela Chiarello, Paola Goatin, Elena Rossi.

F.A. Chiarello's PhD thesis focuses on non-local conservation laws. As a first result, we proved the well-posedness of entropy weak solutions for a class of scalar conservation laws with non-local flux arising in traffic modeling. We approximate the problem by a Lax-Friedrichs scheme and we provide $L^{\infty }$ and BV estimates for the sequence of approximate solutions. Stability with respect to the initial data is obtained from the entropy condition through the doubling of variable technique. The limit model as the kernel support tends to infinity is also studied. See  [33].