Global attractor for a chemotaxis model with prevention of overcrowding

Chemotaxis model with volume filling, introduced by Painter and Hillen is studied under no-flux or Dirichlet boundary conditions. Existence of global-in-time solution to a full model is proved. For some cases existence of a global attractor in the space W-1,W-p (Omega, R-2), p > n, Omega subset of0 R-n is shown. (C) 2004 Elsevier Ltd. All rights reserved.