Mathematical Analysis of a Model for the Initiation of Angiogenesis
Mathematical Analysis of a Model for the Initiation of Angiogenesis
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DOI：
10.1137/s0036141001385046
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
M. Fontelos;A. Friedman;Bei Hu
中科院分区：
文献类型：
--
作者：
M. Fontelos;A. Friedman;Bei Hu
在本文中，我们考虑一个非线性偏微分方程组，由一个抛物线方程和两个关于 t 的常微分方程组成。该系统产生于血管生成的数学模型中，血管生成是从现有血管网络中长出新血管的过程。我们证明系统具有唯一的全局解，并研究其渐近行为$t\rightarrow\infty $。特别是，我们证明平稳解是局部吸引子。
In this paper we consider a nonlinear system of partial differential equations consisting of one parabolic equation and two ordinary differential equations in t. The system arises in a mathematical model of angiogenesis, a process of sprouting of new blood vessels from an existing vascular network. We prove that the system has a unique global solution and study its asymptotic behavior as $t\rightarrow \infty $. In particular, we show that stationary solutions are local attractors.