Global existence and boundedness of classical solutions of the chemotaxis–consumption system nt=Δn−∇⋅(n∇c),0=Δc−nc, under no-flux boundary conditions for n and Robin-type boundary conditions ∂νc=(γ−c)g for c (with γ>0 and C1+β(∂Ω)∋g>0 for some β∈(0,1)) are established in bounded domains Ω⊂RN, N≥1. Under a smallness condition on γ, moreover, we show convergence to the stationary solution.
- Global existence
- Large-time behaviour
- Realistic oxygen boundary conditions