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

Marco Di Francesco, D. Donatelli

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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.
Original languageEnglish
Pages (from-to)79-100
Number of pages22
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number1
Publication statusPublished - 2010

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Copyright 2010 Elsevier B.V., All rights reserved.


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