title: Properties of solutions for a chemotaxis system.
abstract: We investigate mathematically the system of equations proposed by Chaplain and Stuart, to describe the chemotactic response of endothelial cells under the angiogenesis stimulus. In particular, we characterize the steady state endothelial cell density function, and give conditions on the chemotactic parameter k and cell proliferation parameter b that ensure that migration/ proliferation either does or does not occur in steady state. The time dependent problem is also treated.
authors.affiliation: Department of Mathematics, University of Alberta, Edmonton, Canada.
authors.forename: W
authors.initials: W
authors.lastname: Allegretto
authors.forename: H
authors.initials: H
authors.lastname: Xie
authors.forename: S
authors.initials: S
authors.lastname: Yang
mesh_terms: D043925:Angiogenesis Inducing Agents / Q000502:physiology; D000818:Animals; D002633:Chemotaxis; D004730:Endothelium, Vascular / Q000473:pathology; D008433:Mathematics; D008954:Models, Biological; D009374:Neoplasms, Experimental / Q000098:blood supply; D009389:Neovascularization, Pathologic
chemical_list: D043925:Angiogenesis Inducing Agents