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

Benedetto Piccoli (1) , Francesco Rossi (2) , Magali Tournus (3)

1 Rutgers University, Department of Mathematics
2 Dipartimento di Matematica [Padova]
3 I2M - Institut de Mathématiques de Marseille

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.

Mots clés: Signed measures; Kantorovich duality AMS subject classifications 28A33; Transport equation; Kantorovich duality; Wasserstein distance; 35A01

Domaines: Equations aux dérivées partielles [math.AP]

Benedetto Piccoli, Francesco Rossi, Magali Tournus. A Wasserstein norm for signed measures, with application to non local transport equation with source term. 2021. ⟨hal-01665244v5⟩