  In this paper we study a system of nonlinear partial differential equations,
which describes the evolution of two pedestrian groups moving in opposite
direction. The pedestrian dynamics are driven by aversion and cohesion, i.e.
the tendency to follow individuals from the own group and step aside in the
case of contraflow. We start with a 2D lattice based approach, in which the
transition rates reflect the described dynamics, and derive the corresponding
PDE system by formally passing to the limit in the spatial and temporal
discretization. We discuss the existence of special stationary solutions, which
correspond to the formation of directional lanes and prove existence of global
in time bounded weak solutions. The proof is based on an approximation argument
and entropy inequalities. Furthermore we illustrate the behavior of the system
with numerical simulations.

Analysis of PDEs