| Issue |
Math. Model. Nat. Phenom.
Volume 3, Number 7, 2008
Special issue dedicated to Glenn Webb
|
|
|---|---|---|
| Page(s) | 17 - 35 | |
| DOI | https://doi.org/10.1051/mmnp:2008039 | |
| Published online | 23 October 2008 | |
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
1
Mansfield College, University of Oxford, Oxford, UK
2
Dipartimento di Matematica Pura e Applicata, Universita' di Padova, Padova, Italy
3
Department of Mathematics, Vanderbilt University, Nashville, Tennessee
Corresponding author: janet.dyson@mansfield.ox.ac.uk
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.
Mathematics Subject Classification: 92C17 / 92B05 / 92D25 / 47D03 / 47H20 / 35M10
Key words: chemotaxis / global solution / boundedness / nonlocal conditions / diffusion / analytic semigroup / fractional power
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