Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions
Abstract
A system of quasilinear non-uniformly parabolic-elliptic equations
modelling chemotaxis and taking into account the volume filling
effect is studied under no-flux boundary conditions. The proof of
existence and uniqueness of a global-in-time weak solution is given.
First the local solutions are constructed. This is done by the
Schauder fixed point theorem. Uniqueness is proved with the use of
the duality method. A priori estimates are stated either in the case
when the Lyapunov functional is bounded from below or chemotactic
forces are suitably weakened.
modelling chemotaxis and taking into account the volume filling
effect is studied under no-flux boundary conditions. The proof of
existence and uniqueness of a global-in-time weak solution is given.
First the local solutions are constructed. This is done by the
Schauder fixed point theorem. Uniqueness is proved with the use of
the duality method. A priori estimates are stated either in the case
when the Lyapunov functional is bounded from below or chemotactic
forces are suitably weakened.
Keywords
Chemotaxis equations; global-in-time existence and uniqueness; quasilinear reaction-diffusion systems; prevention of blow-up; Schauder fixed point theorem
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