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

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