Well-posedness and stability of a free boundary problem modeling the growth of multi-layer tumors
Well-posedness and stability of a free boundary problem modeling the growth of multi-layer tumors
复制标题
模拟多层肿瘤生长的自由边界问题的适定性和稳定性
DOI：
10.1016/j.jde.2008.02.038
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发表时间：
2008-06
影响因子：
2.4
通讯作者：
Shangbin Cui
中科院分区：
文献类型：
--
作者：
Joachim Escher;Fujun Zhou;Shangbin Cui
本文研究了外部抑制剂作用下多层肿瘤生长的自由边界问题的适定性和稳定性。这个问题的一个重要特点是考虑了自由边界的表面张力。我们首先将这个自由边界问题化为小Hölder空间中的发展方程，并利用抛物型Banach空间中微分方程的适定性理论（即，方程，这是可处理的使用分析半群理论），以证明这个自由边界问题是局部适定的初始数据属于一个小的Hölder空间。接下来我们研究这个问题的平坦解。我们得到了所有平坦的平稳解，并给出了这些平稳解在平坦扰动下的渐近稳定性的精确描述。最后，我们研究了非平坦扰动下平稳解的渐近稳定性。通过对线性化定常问题的谱分析，利用抛物型Banach空间中微分方程的线性化稳定性理论，对所有平坦定常解在非平坦小扰动下的稳定性和不稳定性进行了完整的分析.
In this paper we study well-posedness and stability of a free boundary problem modeling the growth of multi-layer tumors under the action of external inhibitors. An important feature of this problem is that the surface tension of the free boundary is taken into account. We first reduce this free boundary problem into an evolution equation in little Hölder space and use the well-posedness theory for differential equations in Banach spaces of parabolic type (i.e., equations which are treatable by using the analytic semi-group theory) to prove that this free boundary problem is locally well-posed for initial data belonging to a little Hölder space. Next we study flat solutions of this problem. We obtain all flat stationary solutions and give a precise description of asymptotic stability of these stationary solutions under flat perturbations. Finally we investigate asymptotic stability of flat stationary solutions under non-flat perturbations. By carefully analyzing the spectrum of the linearized stationary problem and employing the theory of linearized stability for differential equations in Banach spaces of parabolic type, we give a complete analysis of stability and instability of all flat stationary solutions under small non-flat perturbations.
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影响因子：
2.5
作者：
S. Cui;J. Escher
通讯作者：
S. Cui;J. Escher
影响因子：
2.4
作者：
Friedman, Avner;Hu, Bei
通讯作者：
Hu, Bei
影响因子：
1
作者：
J. Escher
通讯作者：
J. Escher
影响因子：
1.1
作者：
A. Friedman;B. V. Bazaliy
通讯作者：
A. Friedman;B. V. Bazaliy
影响因子：
4.3
作者：
BYRNE, HM;CHAPLAIN, MAJ
通讯作者：
CHAPLAIN, MAJ