Preprint: Diffusive transport on the real line: semi-contractive gradient flows and their discretization
Together with Daniel Matthes and Eva-Maria Rott, we introduce the diffusive transport distance, a novel pseudo-metric between probability measures on the real line. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We observe that certain classes of parabolic PDEs, among them the porous medium equation of exponent two, are formally semi-contractive metric gradient flows in the new distance. This observation is made rigorous for a suitable spatial discretization of the considered PDEs: these are semi-contractive gradient flows with respect to an adapted diffusive transport distance for measures on the point lattice.
Now published in Nonlinearity 38(11), 115005 (2025).
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