Regularity of solutions to a free boundary problem modeling tumor growth by Stokes equation
Regularity of solutions to a free boundary problem modeling tumor growth by Stokes equation
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DOI：
10.1016/j.jmaa.2010.11.028
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发表时间：
2011-05
影响因子：
1.3
通讯作者：
Fujun Zhou;Junde Wu
中科院分区：
文献类型：
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作者：
Fujun Zhou;Junde Wu
在本文中，我们研究的自由边界问题的解决方案的正则性模拟肿瘤生长的流体组织。模型方程包括营养物浓度的准稳态扩散方程，以及具有表示肿瘤细胞的增殖密度的源的Stokes方程，其受到具有受表面张力影响的应力张量的边界条件。该问题是一个包含非局部项的完全非线性问题。本文利用泛函分析方法和极大正则性理论，证明了当初始数据具有较小的正则性时，该问题的自由边界是时空变量真实的解析的。
In this paper we investigate regularity of solutions to a free boundary problem modeling tumor growth in fluid-like tissues. The model equations include a quasi-stationary diffusion equation for the nutrient concentration, and a Stokes equation with a source representing the proliferation density of the tumor cells, subject to a boundary condition with stress tensor effected by surface tension. This problem is a fully nonlinear problem involving nonlocal terms. Based on the employment of the functional analytic method and the theory of maximal regularity, we prove that the free boundary of this problem is real analytic in temporal and spatial variables for initial data of less regularity.