Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model

In the first part of this paper, we investigate thequalitative behavior of classical solutions for aone-dimensional parabolic system derived from a repulsive chemotaxis model onbounded domains. It is shown that classical solutions to theinitial-boundary value problem exist globally in time for large dataand converge to constant equilibrium states exponentially in time. The results indicate that repulsive chemotaxis exhibits a strongtendency against pattern formation. In the second part, we studydiffusion limit and convergence rate of the model toward anon-diffusive problem studied in 11. It is shown thatwhen the chemical diffusion coefficient tends to zero, the solution is convergent in L^-norm with respect to at order O ().