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math.FA2019
Partial differential equations with quadratic nonlinearities viewed as matrix-valued optimal ballistic transport problems
Dmitry Vorotnikov
We study a rather general class of optimal "ballistic" transport problems for matrix-valued measures. These problems naturally arise, in the spirit of \emph{Y. Brenier. Comm. Math.…
math.FA2019
Convex Sobolev inequalities related to unbalanced optimal transport
Stanislav Kondratyev, Dmitry Vorotnikov
We study the behaviour of various Lyapunov functionals (relative entropies) along the solutions of a family of nonlinear drift-diffusion-reaction equations coming from statistical…