Kohlmann Martin
Peter L. Reichertz Institute for Medical Informatics, University of Braunschweig, D-38106 Braunschweig, Germany.
Math Med Biol. 2013 Jun;30(2):175-89. doi: 10.1093/imammb/dqs019. Epub 2012 Feb 29.
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.
本文提出了一种多层肿瘤生长的二维模型。该模型由肿瘤细胞膜的自由边界问题组成，并且假定肿瘤由于细胞增殖或细胞死亡而生长或收缩。生长过程由扩散的营养物质浓度σ引起，并由内部细胞压力p控制。我们假设肿瘤占据一个带状区域，在y = 0处有固定边界，在y = ρ(x)处有自由边界，其中ρ是一个2π周期函数。首先，我们在小赫尔德空间尺度上证明了解(σ, p, ρ)的存在性，并表明我们的模型允许平坦的平稳解。作为主要结果，我们证明了这些平衡点在小扰动下是局部渐近稳定的。
