A multi-species chemotaxis system: Lyapunov functionals, duality, critical mass

作者：Kavallaris N. I.^*; Ricciardi T.; Zecca G.

来源：European Journal of Applied Mathematics, 2018, 29(3): 515-542.

DOI：10.1017/S0956792517000286

• Multi-species chemotaxis models
• Lyapunov functionals
• duality
• logarithmic Hardy-Littlewood-Sobolev inequality
• Moser-Trudinger inequality

We introduce a multi-species chemotaxis type system admitting an arbitrarily large number of population species, all of which are attracted versus repelled by a single chemical substance. The production versus destruction rates of the chemotactic substance by the species is described by a probability measure. For such a model, we investigate the variational structures, in particular, we prove the existence of Lyapunov functionals, we establish duality properties as well as a logarithmic Hardy-Littlewood-Sobolev type inequality for the associated free energy. The latter inequality provides the optimal critical value for the conserved total population mass.

• 出版日期2018-6