Analysis of a mathematical model for the growth of cancer cells

作者：Kohlmann Martin^*

来源：Mathematical Medicine and Biology, 2013, 30(2): 175-189.

DOI：10.1093/imammb/dqs019

• free boundary problem
• tumour growth
• well-posedness
• flat stationary solutions
• stability

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 sigma 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 = rho(x), where rho is a 2 pi-periodic function. First, we prove the existence of solutions (sigma, p, rho) on a scale of small Hoolder 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.

• 出版日期2013-6
• 单位河北医科大学