Analysis of a multispecies cross-diffusion Keller-Segel system with volume filling

Abstract

A chemotaxis-driven multiphase multispecies diffusion system, arising in the formation of vascular-like structures, is analyzed. The model couples porous-medium-type cross-diffusion equations for the volume fractions of the cellular components with multispecies Keller-Segel equations governing the chemoattractant concentrations, posed in a bounded domain with no-flux boundary conditions. The system is derived within a multiphase framework based on mass and force balance laws, together with a characterization of the mixture pressure gradient, which follows from the volume-filling constraint. The existence of a global weak solution, the weak-strong uniqueness property, the exponential decay to the constant steady state, and the vanishing diffusion limit are established. The existence proof extends the boundedness-by-entropy method to solution codomains that are bounded in some directions only, while the other results are based on various entropy estimates and uniform dissipation bounds.