A fitness-driven cross-diffusion system from population dynamics as a gradient flow

• Autor(a) principal: Kondratyev, Stanislav
• Data de Publicação: 2016
• Outros Autores: Monsaingeon, Léonard, Vorotnikov, Dmitry
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/43805; https://doi.org/10.1016/j.jde.2016.05.012

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.