Calculus of Variations and Geometric Measure Theory
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G. Crippa - M. Lecureux-Mercier

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

created by crippa on 27 Jan 2012
modified on 14 Jun 2012


Accepted Paper

Inserted: 27 jan 2012
Last Updated: 14 jun 2012

Journal: Nonlinear Differential Equations and Applications NoDEA
Year: 2011


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


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