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 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 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 …

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 work, we construct and analyze a new fully discrete Lagrangian-Eulerian numerical
method for the treatment of dynamics of conservation laws with nonlocal flux and influence …

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 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 …

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 …