We consider a quasilinear parabolic system which has the structure of Patlak-Keller-Segel model of chemotaxis and contains a class of models with degenerate diffusion. A cell population is described in terms of volume fraction or density. In the latter case, it is assumed that there is a threshold value which the density of cells cannot exceed. Existence and uniqueness of solutions to the corresponding initial-boundary value problem and existence of space inhomogeneous stationary solutions are discussed. In the 1D case a classification of stationary solutions for some model example is provided.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-35,
author = {Dariusz Wrzosek},
title = {Chemotaxis models with a threshold cell density},
journal = {Banach Center Publications},
volume = {83},
year = {2008},
pages = {553-566},
zbl = {1158.35059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-35}
}
Dariusz Wrzosek. Chemotaxis models with a threshold cell density. Banach Center Publications, Tome 83 (2008) pp. 553-566. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc81-0-35/