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 …

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 …

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 …

We consider a class of nonlocal conservation laws with a second-order viscous
regularization term which finds an application in modelling macroscopic traffic flow. The …

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 …

Using a nonlocal second-order traffic flow model we present an approach to control the
dynamics toward a steady state. The system is controlled by the leading vehicle driving at a …

This article designs an optimal observer‐based output feedback control for traffic breakdown
to dissolve traffic congestion using the backstepping method and optimization. The …

This paper studies an optimal tuning of the boundary controller for a heterogeneous traffic
flow model with disturbances in order to alleviate congested traffic. The macroscopic first …

The macroscopic traffic flow model is widely used for traffic control and management. To
incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity …

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 …