# 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

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topDyson, 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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