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arxiv 1910.05105 v1 pith:IXFFG77F submitted 2019-10-11 math.AP

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

Benedetto Piccoli , Francesco Rossi , Magali Tournus (I2M) This is my paper
classification math.AP
keywords measuresnormsignedsourcetransportwassersteinapplicationcondition
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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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