3 papers
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…
math.FA2018
Spherical Hellinger-Kantorovich gradient flows
Stanislav Kondratyev, Dmitry Vorotnikov
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-Kantorovic…
math.AP2016
A fitness-driven cross-diffusion system from polulation dynamics as a gradient flow
Stanislav Kondratyev, Léonard Monsaingeon, Dmitry Vorotnikov
We consider a fitness-driven model of dispersal of interacting populations, which was previously studied merely in the case . Based on some optimal transport distance rece…