A Wasserstein norm for signed measures, with application to non local transport equation with source term
Résumé
We introduce the optimal transportation interpretation of the Kantorovich norm on the
space of signed Radon measures with finite mass, based on a generalized Wasserstein distance
for measures with different masses.
With the formulation and the new topological properties we obtain for this norm, we prove
existence and uniqueness for solutions to non-local transport equations with source terms, when
the initial condition is a signed measure.
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