In this contribution we give a short overview of recent advances in nonlocal conservation
laws. In these equations, we assume that the flux f is decomposable into f (x)= V (x) x, x∈ R …

Nonlocal conservation laws (the signature feature being that the flux function depends on
the solution through the convolution with a given kernel) are extensively used in the …

We deal with the problem of approximating a scalar conservation law by a conservation law
with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential …

We consider a system of nonlocal balance laws where each balance law is coupled with the
remaining balance laws both by a nonlocal velocity function that takes into account the …

We consider a class of nonlocal conservation laws with exponential kernel and prove that
quantities involving the nonlocal term $ W:=\mathbb {1} _ {(-\infty, 0]}(\cdot)\exp …

We study the long-time behaviour of the unique weak solution of a nonlocal regularisation of
the (inviscid) Burgers equation where the velocity is approximated by a one-sided …

We prove the convergence of solutions of nonlocal conservation laws to their local entropic
counterpart for a fundamentally extended class of nonlocal kernels when these kernels …

We study nonlocal conservation laws with a discontinuous flux function of regularity L∞(R)
in the spatial variable and show existence and uniqueness of weak solutions in C ([0, T]; L1 …

In this study, we start from a Follow-the-Leaders model for traffic flow that is based on a
weighted harmonic mean (in Lagrangian coordinates) of the downstream car density. This …

In this article, we present the convergence analysis of a second-order numerical scheme for
traffic flow models that incorporate non-local conservation laws. We combine a MUSCL-type …