Global Existence and Boundedness of Solutions to a Model of Chemotaxis

J. Dyson; R. Villella-Bressan; G. F. Webb

Mathematical Modelling of Natural Phenomena (2008)

  • Volume: 3, Issue: 7, page 17-35
  • ISSN: 0973-5348

Abstract

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A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.

How to cite

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Dyson, J., Villella-Bressan, R., and Webb, G. F.. "Global Existence and Boundedness of Solutions to a Model of Chemotaxis." Mathematical Modelling of Natural Phenomena 3.7 (2008): 17-35. <http://eudml.org/doc/222387>.

@article{Dyson2008,
abstract = { A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant. },
author = {Dyson, J., Villella-Bressan, R., Webb, G. F.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {chemotaxis; global solution; boundedness; nonlocal conditions; diffusion; analytic semigroup; fractional power},
language = {eng},
month = {10},
number = {7},
pages = {17-35},
publisher = {EDP Sciences},
title = {Global Existence and Boundedness of Solutions to a Model of Chemotaxis},
url = {http://eudml.org/doc/222387},
volume = {3},
year = {2008},
}

TY - JOUR
AU - Dyson, J.
AU - Villella-Bressan, R.
AU - Webb, G. F.
TI - Global Existence and Boundedness of Solutions to a Model of Chemotaxis
JO - Mathematical Modelling of Natural Phenomena
DA - 2008/10//
PB - EDP Sciences
VL - 3
IS - 7
SP - 17
EP - 35
AB - A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
LA - eng
KW - chemotaxis; global solution; boundedness; nonlocal conditions; diffusion; analytic semigroup; fractional power
UR - http://eudml.org/doc/222387
ER -

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