A Wasserstein norm for signed measures, with application to non-local transport equation with source term
Benedetto Piccoli, Francesco Rossi, Magali Tournus
Abstract
We introduce the optimal transportation interpretation of the Kantorovich\nnorm on thespace of signed Radon measures with finite mass, based on a\ngeneralized Wasserstein distancefor measures with different masses.With the\nformulation and the new topological properties we obtain for this norm, we\nproveexistence and uniqueness for solutions to non-local transport equations\nwith source terms, whenthe initial condition is a signed measure.\n
Topics & Concepts
Term (time)MathematicsNorm (philosophy)Convection–diffusion equationMathematical analysisApplied mathematicsPhysicsPolitical scienceLawQuantum mechanicsGeometric Analysis and Curvature FlowsPoint processes and geometric inequalitiesTopological and Geometric Data Analysis