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.
Citation
Tomasz Cieślak. Cristian Morale-Rodrigo. "Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions." Topol. Methods Nonlinear Anal. 29 (2) 361 - 381, 2007.
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