@UNPUBLISHED{publication1, title = "Spherical Hellinger-Kantorovich gradient flows", author = "{KONDRATYEV, Stanislav} and {VOROTNIKOV, Dmitry}", year = "2018-09-11", abstract = " We study nonlinear degenerate parabolic equations of Fokker-Planck type which can be viewed as gradient flows with respect to the recently introduced spherical Hellinger-Kantorovich distance. The driving entropy is not assumed to be geodesically convex. We prove solvability of the problem and the entropy-entropy production inequality, which implies exponential convergence to the equilibrium. As a corollary, we obtain some related results for the Wasserstein gradient flows. We also deduce transportation inequalities in the spirit of Talagrand, Otto and Villani for the spherical and conic Hellinger-Kantorovich distances. ", url = "http://www.mat.uc.pt/preprints/eng\_2018.html", note = "" }