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arXiv · 1910.05105

A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term

Benedetto Piccoli·Francesco Rossi·Magali Tournus
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Abstract

We introduce the optimal transportation interpretation of the Kantorovich norm on thespace of signed Radon measures with finite mass, based on a generalized Wasserstein distancefor measures with different masses.With the formulation and the new topological properties we obtain for this norm, we proveexistence and uniqueness for solutions to non-local transport equations with source terms, whenthe initial condition is a signed measure.

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Benedetto Piccoli, Francesco Rossi, Magali Tournus. 2019-10-11. A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term. https://arxiv.org/abs/1910.05105

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