Research

Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding


Reference:

Di Francesco, M. and Rosado, J., 2008. Fully parabolic Keller-Segel model for chemotaxis with prevention of overcrowding. Nonlinearity, 21 (11), pp. 2715-2730.

Related documents:

[img]
Preview
PDF (Author's accepted version) - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (198kB) | Preview

    Official URL:

    http://dx.doi.org/10.1088/0951-7715/21/11/012

    Abstract

    In this paper we study a fully parabolic version of the Keller-Segel system in the presence of a volume filling effect which prevents blow-up of the L norm. This effect is sometimes referred to as prevention of overcrowding. As in the parabolic-elliptic version of this model (previously studied in (Burger et al 2006 SIAM J. Math. Anal. 38 1288-315)), the results in this paper basically infer that the combination of the prevention of the overcrowding effect with a linear diffusion for the density of cells implies domination of the diffusion effect for large times. In particular, first we show that both the density of cells and the concentration of the chemical vanish uniformly for large times, then we prove that the density of cells converges in L1 towards the Gaussian profile of the heat equation as time goes to infinity, at a rate which differs from the rate of convergence to self-similarity for the heat equation by an arbitrarily small constant ('quasi-sharp rate').

    Details

    Item Type Articles
    CreatorsDi Francesco, M.and Rosado, J.
    DOI10.1088/0951-7715/21/11/012
    DepartmentsFaculty of Science > Mathematical Sciences
    Publisher StatementDiFraRosado.pdf: © IOP
    RefereedYes
    StatusPublished
    ID Code32327

    Export

    Actions (login required)

    View Item

    Document Downloads

    More statistics for this item...