A parabolic–elliptic chemotaxis system with non-negative chemotactic sensitivity χ∕v and positive chemical diffusion coefficient η is considered in a smooth bounded domain Ω⊂R N , N≥2 under homogeneous Neumann boundary conditions. We show the existence of at least one global weak solution for χ<χ N , N≥3, where χ N ≔[Formula presented]. Moreover, under further assumptions of Ω and η, we prove that the constructed solution becomes smooth and stabilizes to a constant steady state after some waiting time if N=3,4. The stabilization of a global bounded solution, and the non-existence of non-constant steady states are also discussed in general dimensions.
All Science Journal Classification (ASJC) codes
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics