title: Analysis of a mathematical model for the growth of cancer cells.
abstract: In this paper, a 2D model for the growth of multilayer tumours is presented. The model consists of a free boundary problem for the tumour cell membrane and the tumour is supposed to grow or shrink due to cell proliferation or cell dead. The growth process is caused by a diffusing nutrient concentration σ and is controlled by an internal cell pressure p. We assume that the tumour occupies a strip-like domain with a fixed boundary at y = 0 and a free boundary y = ρ(x), where ρ is a 2π-periodic function. First, we prove the existence of solutions (σ, p, ρ) on a scale of small Höolder spaces and show that our model allows for flat stationary solutions. As a main result, we establish that these equilibrium points are locally asymptotically stable under small perturbations.
authors.affiliation: Peter L. Reichertz Institute for Medical Informatics, University of Braunschweig, D-38106 Braunschweig, Germany. martin.kohlmann@plri.de
authors.forename: Martin
authors.initials: M
authors.lastname: Kohlmann
mesh_terms: D016923:Cell Death; D049109:Cell Proliferation; D005583:Fourier Analysis; D006801:Humans; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D009369:Neoplasms / Q000473:pathology*