We study the existence and uniqueness of the steady state in a model describing the evolution of density of bacteria and oxygen dissolved in water filling a capillary. The steady state is a stationary solution of a nonlinear and nonlocal problem which depends on the energy function and contains two parameters: the total mass of the colony of bacteria and the concentration (or flux) of oxygen at the end of the capillary. The existence and uniqueness of solutions depend on relations between these parameters and the maximum of the energy function.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-1,
author = {Piotr Knosalla and Tadeusz Nadzieja},
title = {Stationary solutions of aerotaxis equations},
journal = {Applicationes Mathematicae},
volume = {42},
year = {2015},
pages = {125-135},
zbl = {1331.92060},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-1}
}
Piotr Knosalla; Tadeusz Nadzieja. Stationary solutions of aerotaxis equations. Applicationes Mathematicae, Tome 42 (2015) pp. 125-135. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-1/