Analysis of a free boundary problem for tumor growth in a periodic external environment

Boundary value problems

Shihe Xu¹ 

[1] School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, P.R. China

关键词: solid avascular tumor;    periodic environment;    stability;    periodic solution;   

DOI  :  10.1186/s13661-015-0399-0

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper a free boundary problem for solid avascular tumor growth in a periodic external environment is studied. The periodic environment means that the supply of nutrient and inhibitors is periodic. Sufficient conditions for the global stability of tumor free equilibrium are given. We also prove that if external concentration of nutrients is large, the tumor will not disappear. The conditions under which there exists a unique periodic solution to the model are determined, and we also show that the unique periodic solution is a global attractor of all other positive solutions.

【 授权许可】

CC BY