Global existence of solutions to a chemotaxis system with volume filling effect

Volume 111 / 2008

Tomasz Cieślak Colloquium Mathematicum 111 (2008), 117-134 MSC: 92C17, 35K65, 35K67. DOI: 10.4064/cm111-1-11


A system of quasilinear parabolic equations modelling chemotaxis and taking into account the volume filling effect is studied under no-flux boundary conditions. The resulting system is non-uniformly parabolic. A Lyapunov functional for the system is constructed. The proof of existence and uniqueness of regular global-in-time solutions is given in cases when either the Lyapunov functional is bounded from below or chemotactic forces are suitably weakened. In the first case solutions are uniformly bounded in time, in the second one it is shown that a uniform bound is not possible.


  • Tomasz CieślakInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    P.O. Box 21
    00-956 Warszawa, Poland

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