Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow

Gianluca Crippa (1) , Magali Lécureux-Mercier (2)

1 Department of Mathematics [Basel]
2 TECHNION - Department of Mathematics

In this paper, we prove existence and uniqueness of measure solutions for the Cauchy problem associated to the (vectorial) continuity equation with a non-local flow. We also give a stability result with respect to various parameters.

Mots clés: pedestrian traffic; System of conservation laws; continuity equations; Wasserstein distance; nonlocal flow; pedestrian traffic.

Domaines: Equations aux dérivées partielles [math.AP]

Gianluca Crippa, Magali Lécureux-Mercier. Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow. 2011. ⟨hal-00653053⟩