A HELE-SHAW problem for tumor growth
A HELE-SHAW problem for tumor growth
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肿瘤生长的 HELE-SHAW 问题
DOI：
10.1016/j.jfa.2017.08.009
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
F. Quirós
中科院分区：
文献类型：
--
作者：
A. Mellet;B. Perthame;F. Quirós
我们考虑对一个模拟肿瘤生长的问题的弱解决方案。在初始数据满足一定条件下，通过求解描述癌细胞数密度演化的Lotka-Volterra源项的多孔介质类问题的刚性(不可压缩)极限即可得到解。我们证明了这种极限解解决了一个Hele-Shaw型自由边界问题。我们还得到了解的正则性和自由边界的正则性，主要的新困难来自于保持初始奇性的源增长和具有正则化效应的侵入区域的自由边界之间的竞争。新的岛屿可以在非常时期产生。
We consider weak solutions to a problem modeling tumor growth. Under certain conditions on the initial data, solutions can be obtained by passing to the stiff (incompressible) limit in a porous medium type problem with a Lotka–Volterra source term describing the evolution of the number density of cancerous cells. We prove that such limit solutions solve a free boundary problem of Hele–Shaw type. We also obtain regularity properties, both for the solution and for its free boundary.The main new difficulty arises from the competition between the growth due to the source, which keeps the initial singularities, and the free boundary which invades the domain with a regularizing effect. New islands can be generated at singular times.
影响因子：
5.3
作者：
Ding J;Ali F;Chen G;Li H;Mahuku G;Yang N;Narro L;Magorokosho C;Makumbi D;Yan J
通讯作者：
Yan J