Nonlinear diffusion: Geodesic Convexity is equivalent to Wasserstein Contraction

Abstract

It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Under suitable convexity conditions on the nonlinearity, due to R. J. McCann [10], the associated entropy is geodesically convex, which implies a contraction type property between… (More)

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