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Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions

 

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Opened Access Quasilinear non-uniformly parabolic-elliptic system modelling chemotaxis with volume filling effect. Existence and uniqueness of global-in-time solutions
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Author: Cieslak, Tomasz
Morales Rodrigo, Cristian
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2007
Published in: Topological Methods in Nonlinear Analysis, 29 (2), 361-381.
Document type: Article
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.
Cite: Cieslak, T. y Morales Rodrigo, C. (2007). 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, 29 (2), 361-381.
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URI: http://hdl.handle.net/11441/42193

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