Abstract
This paper extends the volume filling chemotaxis model [18, 26] by taking into account the cell population interactions. The extended chemotaxis models have nonlinear diffusion and chemotactic sensitivity depending on cell population density, which is a modification of the classical Keller-Segel model in which the diffusion and chemotactic sensitivity are constants (linear). The existence and boundedness of global solutions of these models are discussed and the numerical pattern formations are shown. The further improvement is proposed in the end.
Original language | English |
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Pages (from-to) | 173-190 |
Number of pages | 18 |
Journal | Mathematical Modelling of Natural Phenomena |
Volume | 5 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 2010 |
Externally published | Yes |
Keywords
- blow up
- cell interactions
- chemotactic sensitivity
- chemotaxis
- Keller-Segel model
- nonlinear diffusion
- pattern formation
- volume filling
ASJC Scopus subject areas
- Modelling and Simulation