title: Equilibrium model of a vascularized spherical carcinoma with central necrosis--some properties of the solution.
abstract: Properties of the solutions of a nonlinear time-independent diffusion equation are studied. The equation arises in a model of a spherically symmetric vascularized carcinoma with a central necrotic core. The boundary value problem as posed possesses a constant solution when the nutrient consumption rate and deposition rate (from the vascular network) are equal. This solution can lose uniqueness at a critical tumor dimension which corresponds to the onset of instability with respect to deviations from that uniform equilibrium state.
authors.affiliation: Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA 23529-0077.
authors.forename: J A
authors.initials: JA
authors.lastname: Adam
authors.forename: R D
authors.initials: RD
authors.lastname: Noren
mesh_terms: D002455:Cell Division; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009336:Necrosis; D009369:Neoplasms / Q000098:blood supply* / Q000473:pathology*