Inserted: 27 jan 2012
Last Updated: 14 jun 2012
Journal: Nonlinear Differential Equations and Applications NoDEA
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.
Keywords: Wasserstein distance, System of conservation laws, continuity equations, nonlocal flow, pedestrian traffic