# American Institute of Mathematical Sciences

November  2013, 12(6): 3027-3046. doi: 10.3934/cpaa.2013.12.3027

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

 1 Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong 2 Department of Mathematics, Tulane University, New Orleans, LA 70118

Received  April 2012 Revised  November 2013 Published  May 2013

In the first part of this paper, we investigate the qualitative behavior of classical solutions for a one-dimensional parabolic system derived from a repulsive chemotaxis model on bounded domains. It is shown that classical solutions to the initial-boundary value problem exist globally in time for large data and converge to constant equilibrium states exponentially in time. The results indicate that repulsive chemotaxis exhibits a strong tendency against pattern formation. In the second part, we study diffusion limit and convergence rate of the model toward a non-diffusive problem studied in [11]. It is shown that when the chemical diffusion coefficient $\varepsilon$ tends to zero, the solution is convergent in $L^{\infty}$-norm with respect to $\varepsilon$ at order $O(\varepsilon)$.
Citation: Zhi-An Wang, Kun Zhao. Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model. Communications on Pure & Applied Analysis, 2013, 12 (6) : 3027-3046. doi: 10.3934/cpaa.2013.12.3027
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