Global attractor for a chemotaxis model with prevention of overcrowding Original Research Article

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 W1,p(Ω,R2),p>n,Ω⊂RnW1,p(Ω,R2),p>n,Ω⊂Rn is shown.