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.
|Number of pages||30|
|Journal||SIAM Journal on Mathematical Analysis (SIMA)|
|Early online date||30 Nov 2010|
|Publication status||Published - 2010|