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 …

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 …

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 study a class of nonlinear nonlocal conservation laws with discontinuous flux, modeling
crowd dynamics and traffic flow. The discontinuous coefficient of the flux function is assumed …

We deal with the numerical investigation of the local limit of nonlocal conservation laws.
Previous numerical experiments seem to suggest that the solutions of the nonlocal problems …

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 …

Consider a non-local (ie, involving a convolution term) conservation law: when the
convolution term converges to a Dirac delta, in the limit we formally recover a classical (or" …

In this paper, we introduce a non-local PDE-ODE traffic model devoted to the description of a
1-to-1 junction with buffer. We present a numerical method to approximate solutions and …

We study the turnpike phenomenon for optimal control problems with mean-field dynamics
that are obtained as the limit of ordinary differential equations. We show that the optimal …