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Singular convergence of nonlinear hyperbolic chemotaxis systems to keller-segel type models


Reference:

Di Francesco, M. and Donatelli, D., 2010. Singular convergence of nonlinear hyperbolic chemotaxis systems to keller-segel type models. Discrete and Continuous Dynamical Systems - Series B, 13 (1), pp. 79-100.

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    Official URL:

    http://dx.doi.org/10.3934/dcdsb.2010.13.79

    Abstract

    In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller-Segel type systems. The approximating systems are either hyperbolicparabolic or hyperbolic-elliptic. They all feature a nonlinear pressure term arising from a volume filling effect which takes into account the fact that cells do not interpenetrate. The main convergence result relies on energy methods and compensated compactness tools and is obtained for large initial data under suitable assumptions on the approximating solutions. In order to justify such assumptions, we also prove an existence result for initial data which are small perturbation of a constant state. Such result is proven via classical Friedrichs's symmetrization and linearization. In order to simplify the coverage, we restrict to the two-dimensional case with periodical boundary conditions.

    Details

    Item Type Articles
    CreatorsDi Francesco, M.and Donatelli, D.
    DOI10.3934/dcdsb.2010.13.79
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code32325
    Additional InformationCopyright 2010 Elsevier B.V., All rights reserved.

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