# American Institute of Mathematical Sciences

May  2016, 21(3): 997-1008. doi: 10.3934/dcdsb.2016.21.997

## Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients

 1 Department of Mathematics, Zhaoqing University, Zhaoqing, 526061 2 College of Mathematics and Informatics, South China Agricultural University, Guangzhou, Guangdong 510642, China 3 School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061, China

Received  July 2015 Revised  September 2015 Published  January 2016

In this paper we study a free boundary problem for the growth of avascular tumors. The establishment of the model is based on the diffusion of nutrient and mass conservation for the two process proliferation and apoptosis(cell death due to aging). It is assumed the supply of external nutrients is periodic. We mainly study the long time behavior of the solution, and prove that in the case $c$ is sufficiently small, the volume of the tumor cannot expand unlimitedly. It will either disappear or evolve to a positive periodic state.
Citation: Shihe Xu, Yinhui Chen, Meng Bai. Analysis of a free boundary problem for avascular tumor growth with a periodic supply of nutrients. Discrete & Continuous Dynamical Systems - B, 2016, 21 (3) : 997-1008. doi: 10.3934/dcdsb.2016.21.997
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