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

Shihe Xu; Yinhui  Chen; Meng  Bai

doi:10.3934/dcdsb.2016.21.997

Article Contents

2016, Volume 21, Issue 3: 997-1008. Doi: 10.3934/dcdsb.2016.21.997

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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
3.
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong 526061

Received: July 2015

Revised: September 2015

Published: May 2016

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K57, 35K20; Secondary: 35B10.

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