Asymptotic stability for a free boundary problem arising in a tumor model
Asymptotic stability for a free boundary problem arising in a tumor model
复制标题
DOI：
10.1016/j.jde.2005.09.008
复制
发表时间：
2006-08-15
影响因子：
2.4
通讯作者：
Hu, Bei
中科院分区：
文献类型：
--
作者：
Friedman, Avner;Hu, Bei
我们考虑一个肿瘤模型，其中所有细胞都以一定的速率增殖，它们的密度与营养物质浓度成正比。该模型由椭圆方程和抛物方程的耦合系统组成，肿瘤边界为自由边界。已知，对于适当的参数选择，存在一个唯一的、与之无关的半径为R-S的球对称平稳解。最近证明了存在一个函数mu(*)(RS)，使得当mu < mu(*)（RS）时球面平稳解线性稳定，当mu > mu(*)（RS）时线性不稳定。本文证明了当mu < mu(*)（RS）时，球面平稳解是非线性稳定的（或渐近稳定的）。(c) 2005爱思唯尔公司版权所有。
We consider a tumor model in which all cells are proliferating at a rate mu and their density is proportional to the nutrient concentration. The model consists of a coupled system of an elliptic equation and a parabolic equation, with the tumor boundary as a free boundary. It is known that for an appropriate choice of parameters, there exists a unique spherically symmetric stationary solution with radius R-S which is independent of it. It was recently proved that there is a function mu(*)(RS) such that the spherical stationary solution is linearly stable if mu < mu(*)(RS) and linearly unstable if mu > mu(*)(RS). In this paper we prove that the spherical stationary solution is nonlinearly stable (or, asymptotically stable) if mu < mu(*)(RS). (c) 2005 Elsevier Inc. All rights reserved.