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December  2006, 5(4): 779-792. doi: 10.3934/cpaa.2006.5.779

The behavior of the solution for a mathematical model for analysis of the cell cycle

Yu-Hsien Chang 1, and  Guo-Chin Jau 2,

1. 

Department of Mathematics, National Taiwan Normal University, 88 Sec. 4, Ting Chou Road, Taipei, Taiwan
2. 

Department of Mathematics and Computer Science Education, Taipei Municipal University of Education, 1, Ai-Kuo West Road, Taipei, Taiwan 100, R. O. C., Taiwan

Received  February 2006 Revised  May 2006 Published  September 2006

The treatment by radiotherapy or chemotherapy to human cancers induces a complex chain of events involving reversible cell cycle and cell death [1]. In this paper we study the asymptotical behavior of the solutions for the mathematical model that has potential to describe the growth of human tumors cells and their responses to therapy. We found that the solutions of this system are either bounded, exponential bounded or exponential decay. This result can be used to predict the response of cells to mitotic arrest.
Keywords: Fourier analysis, Duhamel's principle., Gronwall's inequality, Fixed point theorem.
Mathematics Subject Classification: 3.
Citation: Yu-Hsien Chang, Guo-Chin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure & Applied Analysis, 2006, 5 (4) : 779-792. doi: 10.3934/cpaa.2006.5.779
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