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 …

In this paper we develop a family of very high-order central (up to 6th-order) non-oscillatory
schemes for mixed-element unstructured meshes. The schemes are inherently compact in …

We give an overview of mathematical traffic flow models with non-local velocity. More
precisely, we consider conservation laws with flux functions depending on an integral …

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 …

In this work we present a rather general approach to approximate the solutions of nonlocal
conservation laws. In a first step, we approximate the nonlocal term with an appropriate …

In this paper, we propose and analyze a reconstruction technique which enables one to
design high-order conservative semi-Lagrangian schemes for kinetic equations. The …

In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic
equations. They are based on the conservative reconstruction technique introduced in [1] …

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 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 …