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

• Autorzy: Tomasz Cieślak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35K67: Singular parabolic equations
• 35K65: Degenerate parabolic equations
• 92C17: Cell movement (chemotaxis, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 111
• Numer: 1
• Strony: 117-134

Daty

wydano

2008

Twórcy

autor

Tomasz Cieślak

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

Identyfikatory

DOI

10.4064/cm111-1-11