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 …

Hyperbolic systems model the phenomena of propagations at finite speeds. They are
present in many fields of science and, consequently, in many human applications. For these …

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 conservation laws with nonlocal velocity and show, for nonlocal weights of
exponential type, that the unique solutions converge in a weak or strong sense (dependent …

In this note, we extend the known results on the existence and uniqueness of weak solutions
to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution …

In this contribution, we study the singular limit problem of a nonlocal conservation law with a
discontinuity in space. The corresponding local equation can be transformed …

We present a network formulation for a traffic flow model with nonlocal velocity in the flux
function. The modeling framework includes suitable coupling conditions at intersections to …

We present a convergence result from nonlocal to local behavior for a system of nonlocal
balance laws. The velocity field of the underlying conservation laws is diagonal. In contrast …

We present a multilane traffic model based on balance laws, where the nonlocal source term
is used to describe the lane changing rate. The modelling framework includes the …

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 …