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March 2008 Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions
Martin Burger, Yasmin Dolak-Struss, Christian Schmeiser
Commun. Math. Sci. 6(1): 1-28 (March 2008).


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.


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Martin Burger. Yasmin Dolak-Struss. Christian Schmeiser. "Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions." Commun. Math. Sci. 6 (1) 1 - 28, March 2008.


Published: March 2008
First available in Project Euclid: 7 March 2008

zbMATH: 1165.35471
MathSciNet: MR2397995

Primary: 35Q80 , 35R35 , 92C17

Keywords: asymptotic behavior , chemotaxis models , Interface motion , surface diffusion

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 1 • March 2008
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