Nonlinear Cross-Diffusion with Size Exclusion

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 1. Introduction. Modelling the transport of particles with size exclusion is of high relevance in many current applications, e.g., in molecular and cell biology. In the case of a single type of particle, various models have been proposed at the continuum level or derived from microscopic models (cf. [25, 42]), typically leading to nonlinear drift-diffusion equations for the particle density of the form