The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion efects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates signicant 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, in particular we characterize the large-time behaviour of solutions.

@TechReport{BDPS10,
  author       = {Burger, M. and Di Francesco, M. and Pietschmann, J.-F. and Schlake, B.},
  title        = {Nonlinear cross-diffusion with size exclusion},
  institution  = {WWU M?nster},
  year         = {2010},
  url          = \{/2010/BDPS10},
}