NON-LOCAL SCALAR CONSERVATION LAWS WITH CONGESTION - FEDERICO STRA - POLITECNICO DI TORINO
In this seminar I present a recent result obtained in collaboration with Emanuela Radici (EPFL). We studied a deterministic particle scheme (Lagrangian discretization) to solve non-local scalar conservation laws with congestion in one dimension. We show that the discrete approximations con- verge to the unique entropy solution under more general assumptions that the existing literature: the velocity fields are less regular (in particular the interaction force can have a discontinuity at the origin), there are no prescribed attractive/repulsive regimes, and the mobility can have unbounded support. I then give a summary of several possible future developments, focusing in particular on a brief description of an undergoing work in collaboration with Emanuela Radici and Elio Marconi (EPFL) about the stability of “almostentropy solutions” of scalar conservation laws.