Well-posedness and Stability of a Multi-dimensional Tumor Growth Model
Well-posedness and Stability of a Multi-dimensional Tumor Growth Model
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DOI：
10.1007/s00205-008-0158-9
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发表时间：
2009
影响因子：
2.5
通讯作者：
S. Cui;J. Escher
中科院分区：
文献类型：
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作者：
S. Cui;J. Escher
我们研究了一个移动边界问题模拟体外肿瘤的生长。该问题由两个椭圆方程和一个一阶偏微分方程组成，椭圆方程分别描述营养物和内压的分布，一阶偏微分方程描述动边界的演化。一个重要的特点是考虑了表面张力对移动边界的影响。我们证明了这个问题是局部适定的一个大类的初始数据，通过使用分析半群理论。我们还证明了当表面张力系数γ大于阈值γ* 时，唯一的平面平衡点是渐近稳定的，而当γ<γ* 时，这个平面平衡点是不稳定的.
We study a moving boundary problem modeling the growth of in vitro tumors. This problem consists of two elliptic equations describing the distribution of the nutrient and the internal pressure, respectively, and a first-order partial differential equation describing the evolution of the moving boundary. An important feature is that the effect of surface tension on the moving boundary is taken into account. We show that this problem is locally well-posed for a large class of initial data by using analytic semi-group theory. We also prove that if the surface tension coefficient γ is larger than a threshold valueγ*then the unique flat equilibrium is asymptotically stable, whereas in the caseγ<γ*this flat equilibrium is unstable.