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 two- and three-dimensional domains.
@article{1204905775,
author = {Burger, Martin and Dolak-Struss, Yasmin and Schmeiser, Christian},
title = {Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions},
journal = {Commun. Math. Sci.},
volume = {6},
number = {1},
year = {2008},
pages = { 1-28},
language = {en},
url = {http://dml.mathdoc.fr/item/1204905775}
}
Burger, Martin; Dolak-Struss, Yasmin; Schmeiser, Christian. Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions. Commun. Math. Sci., Tome 6 (2008) no. 1, pp. 1-28. http://gdmltest.u-ga.fr/item/1204905775/