Geodesic
Global existence of solutions to a chemotaxis system with volume filling effect
Tomasz Cieślak1
1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21 00-956 Warszawa, Poland
Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 117-134

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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.
DOI : 10.4064/cm111-1-11
Keywords: system quasilinear parabolic equations modelling chemotaxis taking account volume filling effect studied under no flux boundary conditions resulting system non uniformly parabolic lyapunov functional system constructed proof existence uniqueness regular global in time solutions given cases either lyapunov functional bounded below chemotactic forces suitably weakened first solutions uniformly bounded time second shown uniform bound possible

Tomasz Cieślak 1

1 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 P.O. Box 21 00-956 Warszawa, Poland 
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Tomasz Cieślak. Global existence of solutions to a chemotaxis
 system with volume filling effect. Colloquium Mathematicum, Tome 111 (2008) no. 1, pp. 117-134. doi: 10.4064/cm111-1-11

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