Synchronization of weakly coupled oscillators is ubiquitous in biological and chemical
complex systems. Recently, research on collective dynamics of many-body systems has …

This book presents mathematical models and numerical simulations of crowd dynamics. The
core topic is the development of a new multiscale paradigm, which bridges the microscopic …

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 present a new class of macroscopic models for pedestrian flows. Each individual is
assumed to move towards a fixed target, deviating from the best path according to the …

We prove the well-posedness of entropy weak solutions of a scalar conservation law with
non-local flux arising in traffic flow modeling. The result is obtained providing accurate L^ ∞ …

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 …

We consider an extension of the traffic flow model proposed by Lighthill, Whitham and
Richards, in which the mean velocity depends on a weighted mean of the downstream traffic …

This paper develops the basic analytical theory related to some recently introduced crowd
dynamics models. Where well posedness was known only locally in time, it is here extended …

The well-known kinematic sedimentation model by Kynch states that the settling velocity of
small equal-sized particles in a viscous fluid is a function of the local solids volume fraction …

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 …