A fitness-driven cross-diffusion system from population dynamics as a gradient flow
Journal of Differential Equations(2016)
Abstract
We consider a fitness-driven model of dispersal of N interacting populations, which was previously studied merely in the case N=1. Based on some optimal transport distance recently introduced, we identify the model as a gradient flow in the metric space of Radon measures. We prove existence of global non-negative weak solutions to the corresponding system of parabolic PDEs, which involves degenerate cross-diffusion. Under some additional hypotheses and using a new multicomponent Poincaré–Beckner functional inequality, we show that the solutions converge exponentially to an ideal free distribution in the long time regime.
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35K51,35K65,35Q92,49Q20,58B20,92D40
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