THE TRANSPORT of electrical energy, the flow of fluids in open channels or in gas
pipelines, the light propagation in optical fibres, the motion of chemicals in plug flow …

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 consider a supply chain consisting of a sequence of buffer queues and processors with
certain throughput times and capacities. Based on a simple rule for releasing parts, ie …

We present an epidemic model capable of describing key features of the Covid-19
pandemic. While capturing several qualitative properties of the virus spreading, it allows to …

We consider a class of nonlocal balance laws as initial value problems on a finite time
horizon and show existence and uniqueness of the corresponding weak solutions. The …

This paper focuses on the analytical properties of the solutions to the continuity equation
with non local flow. Our driving examples are a supply chain model and an equation for the …

We present a Godunov type numerical scheme for a class of scalar conservation laws with
non-local flux arising for example in traffic flow models. The proposed scheme delivers more …

We show that for monotone initial datum the solution of nonlocal conservation laws
converges to the entropy solution of the corresponding local conservation laws when the …

We consider a nonlocal conservation law on a bounded spatial domain and show existence
and uniqueness of weak solutions for nonnegative flux function and left-hand-side boundary …

In this article, we generalize some existence and uniqueness results in [22] for scalar
nonlocal balance laws to multi-dimensional nonlocal balance laws. Also in the multi …