title: A non-local evolution equation model of cell-cell adhesion in higher dimensional space.
abstract: A model for cell-cell adhesion, based on an equation originally proposed by Armstrong et al. [A continuum approach to modelling cell-cell adhesion, J. Theor. Biol. 243 (2006), pp. 98-113], is considered. The model consists of a nonlinear partial differential equation for the cell density in an N-dimensional infinite domain. It has a non-local flux term which models the component of cell motion attributable to cells having formed bonds with other nearby cells. Using the theory of fractional powers of analytic semigroup generators and working in spaces with bounded uniformly continuous derivatives, the local existence of classical solutions is proved. Positivity and boundedness of solutions is then established, leading to global existence of solutions. Finally, the asymptotic behaviour of solutions about the spatially uniform state is considered. The model is illustrated by simulations that can be applied to in vitro wound closure experiments.
authors.affiliation: a Mansfield College , University of Oxford , Oxford OX1 3TF , UK.
authors.forename: Janet
authors.initials: J
authors.lastname: Dyson
authors.forename: Stephen A
authors.initials: SA
authors.lastname: Gourley
authors.forename: Glenn F
authors.initials: GF
authors.lastname: Webb
mesh_terms: D002448:Cell Adhesion; D002450:Cell Communication; D002465:Cell Movement; D049109:Cell Proliferation; D003198:Computer Simulation; D015509:Developmental Biology; D004058:Diffusion; D006801:Humans; D016014:Linear Models; D008954:Models, Biological; D009038:Motion; D009361:Neoplasm Invasiveness; D009369:Neoplasms / Q000378:metabolism; D014945:Wound Healing