On Chemotaxis Models with Cell Population Interactions

Z. A. Wang

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 3, page 173-190
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Wang, Z. A.. "On Chemotaxis Models with Cell Population Interactions." Mathematical Modelling of Natural Phenomena 5.3 (2010): 173-190. <http://eudml.org/doc/197722>.

@article{Wang2010,
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.},
author = {Wang, Z. A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {chemotaxis; Keller-Segel model; cell interactions; nonlinear diffusion; blow up; volume filling; chemotactic sensitivity; pattern formation},
language = {eng},
month = {4},
number = {3},
pages = {173-190},
publisher = {EDP Sciences},
title = {On Chemotaxis Models with Cell Population Interactions},
url = {http://eudml.org/doc/197722},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Wang, Z. A.
TI - On Chemotaxis Models with Cell Population Interactions
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/4//
PB - EDP Sciences
VL - 5
IS - 3
SP - 173
EP - 190
AB - 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.
LA - eng
KW - chemotaxis; Keller-Segel model; cell interactions; nonlinear diffusion; blow up; volume filling; chemotactic sensitivity; pattern formation
UR - http://eudml.org/doc/197722
ER -

References

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