Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions
Keywords
Chemotaxis equations, global-in-time existence and uniqueness, quasilinear reaction-diffusion systems, prevention of blow-up, Schauder fixed point theoremAbstract
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.Downloads
Published
2007-06-01
How to Cite
1.
CIEŚLAK, Tomasz and MORALE-RODRIGO, Cristian. Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions. Topological Methods in Nonlinear Analysis. Online. 1 June 2007. Vol. 29, no. 2, pp. 361 - 381. [Accessed 24 April 2024].
Issue
Section
Articles
Stats
Number of views and downloads: 0
Number of citations: 0