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

par Magali Tournus (Institut Mathématique de Marseille)

mardi 12 févr. 2019, 15:00 → 16:00 Europe/Paris

Salle 435 (UMPA/ENS de Lyon)

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 and non-linear transport equations with source terms, when the initial condition is a signed measure.