Existence result for a two-dimensional system of conservation laws with unilateral constraints

The aim of this paper is to study a pressureless model with unilateral constraint in two dimensions. The corresponding one-dimensional case is a traffic flow model and was studied in [8]. The two-dimensional extension is linked to pedestrian flow. Several difficulties, geometric and analytical, appear with respect to the one-dimensional case. We get the existence of weak solutions for general initial data and the constraints in a strong sense.