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This paper is devoted to a study of the asymptotic behavior of solutions of a chemotaxis model with logistic terms in multiple spatial dimensions. Of particular interest is the practically relevant case of small diffusivity, where (as in the one-dimensional case) the cell densities form plateau-like solutions for large time. The major difference from the one-dimensional case is the motion of these plateau-like solutions. with respect to the plateau boundaries separating zero density regions from maximum density regions. This interface motion appears on a non-logarithmic time scale and can be interpreted as a surface diffusion law. The biological interpretation of the surface diffusion is that a packed region of cells can change its shape mainly if cells diffuse along its boundary. The theoretical results on the asymptotic behavior are supplemented by several numerical simulations on twoand three-dimensional domains.

Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions