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

Previous Article
Global solution to a phase transition model with microscopic movements and accelerations in one space dimension
CPAA Home
This Issue
Next Article
Minimax and viscosity solutions of Hamilton-Jacobi equations in the convex case

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

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

Abstract
Related Papers

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

[1]	Shui-Hung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692-697. doi: 10.3934/proc.2011.2011.692
[2]	Rabah Amir, Igor V. Evstigneev. On Zermelo's theorem. Journal of Dynamics & Games, 2017, 4 (3) : 191-194. doi: 10.3934/jdg.2017011
[3]	John Hubbard, Yulij Ilyashenko. A proof of Kolmogorov's theorem. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 367-385. doi: 10.3934/dcds.2004.10.367
[4]	Felipe Riquelme. Ruelle's inequality in negative curvature. Discrete & Continuous Dynamical Systems - A, 2018, 38 (6) : 2809-2825. doi: 10.3934/dcds.2018119
[5]	S. S. Dragomir, C. E. M. Pearce. Jensen's inequality for quasiconvex functions. Numerical Algebra, Control & Optimization, 2012, 2 (2) : 279-291. doi: 10.3934/naco.2012.2.279
[6]	Hahng-Yun Chu, Se-Hyun Ku, Jong-Suh Park. Conley's theorem for dispersive systems. Discrete & Continuous Dynamical Systems - S, 2015, 8 (2) : 313-321. doi: 10.3934/dcdss.2015.8.313
[7]	Sergei Ivanov. On Helly's theorem in geodesic spaces. Electronic Research Announcements, 2014, 21: 109-112. doi: 10.3934/era.2014.21.109
[8]	Torsten Lindström. Discrete models and Fisher's maximum principle in ecology. Conference Publications, 2003, 2003 (Special) : 571-579. doi: 10.3934/proc.2003.2003.571
[9]	Pablo Raúl Stinga, Chao Zhang. Harnack's inequality for fractional nonlocal equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (7) : 3153-3170. doi: 10.3934/dcds.2013.33.3153
[10]	V. Niţicâ. Journé's theorem for $C^{n,\omega}$ regularity. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 413-425. doi: 10.3934/dcds.2008.22.413
[11]	Jacques Féjoz. On "Arnold's theorem" on the stability of the solar system. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3555-3565. doi: 10.3934/dcds.2013.33.3555
[12]	Dmitry Kleinbock, Barak Weiss. Dirichlet's theorem on diophantine approximation and homogeneous flows. Journal of Modern Dynamics, 2008, 2 (1) : 43-62. doi: 10.3934/jmd.2008.2.43
[13]	Lena Noethen, Sebastian Walcher. Tikhonov's theorem and quasi-steady state. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 945-961. doi: 10.3934/dcdsb.2011.16.945
[14]	Fatiha Alabau-Boussouira, Piermarco Cannarsa. A constructive proof of Gibson's stability theorem. Discrete & Continuous Dynamical Systems - S, 2013, 6 (3) : 611-617. doi: 10.3934/dcdss.2013.6.611
[15]	Koray Karabina, Edward Knapp, Alfred Menezes. Generalizations of Verheul's theorem to asymmetric pairings. Advances in Mathematics of Communications, 2013, 7 (1) : 103-111. doi: 10.3934/amc.2013.7.103
[16]	Mateusz Krukowski. Arzelà-Ascoli's theorem in uniform spaces. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 283-294. doi: 10.3934/dcdsb.2018020
[17]	Shalosh B. Ekhad and Doron Zeilberger. Proof of Conway's lost cosmological theorem. Electronic Research Announcements, 1997, 3: 78-82.
[18]	Florian Wagener. A parametrised version of Moser's modifying terms theorem. Discrete & Continuous Dynamical Systems - S, 2010, 3 (4) : 719-768. doi: 10.3934/dcdss.2010.3.719
[19]	Pengyan Wang, Pengcheng Niu. Liouville's theorem for a fractional elliptic system. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1545-1558. doi: 10.3934/dcds.2019067
[20]	Joseph J Kohn. Nirenberg's contributions to complex analysis. Discrete & Continuous Dynamical Systems - A, 2011, 30 (2) : 537-545. doi: 10.3934/dcds.2011.30.537

2018 Impact Factor: 0.925

American Institute of Mathematical Sciences