| Abstract: |
| We interpret a class of nonlinear Fokker-Planck equations with reaction as gradient flows over the space of Radon measures equipped with the recently introduced HK-distance \cite{1}-\cite{3} and the spherical HK-distance \cite{4}. We prove new isoperimetric-type functional inequalities, which allow us to control the relative entropy by its production. We establish the entropic exponential convergence of the trajectories of the flow to the equilibrium. Along with other applications, this result has an ecological interpretation as a trend to the ideal free distribution for a class of fitness-driven models of population dynamics.
Based on a joint work with S. Kondratyev.
\begin{thebibliography}{99}
\bibitem{1} S. Kondratyev, L. Monsaingeon, D. Vorotnikov, A new optimal transport distance on the space of finite Radon measures, Adv. Differential Equations 21 (2016) 1117-1164.
\bibitem{2} M. Liero, A. Mielke, G. Savar\`e, Optimal entropy-transport problems and a new Hellinger-Kantorovich distance between positive measures, to appear in Invent. Math.
\bibitem{3} L. Chizat et al. An Interpolating Distance Between Optimal Transport and Fisher-Rao Metrics, to appear in Found. Comp. Math.
\bibitem{4} A. Mielke and V. Laschos. Geometric properties of cones with applications on the Hellinger-Kantorovich space, and a new distance on the space of probability measures, preprint.
\end{thebibliography} |
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