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Existence and stability of a constant stationary solution for a simplified tumor growth model

Journal Name:

  • Mathematica Æterna

Publication Year:

  • 2012

Key Words:

Author Name
Abstract (2. Language): 
The aim of this paper is to study a problem of existence and stability related to a tumor growth mathematical model. Based on a classical mathematical model for tumor growth describing proliferating, quiescent and necrotic cells, we propose to calculate explicitly the stationary solution and discuss the stability with respect to these three cells. Some open problems are presented in the conclusion.
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  • English

REFERENCES

References: 

[1] J.A. Adam, A simplified mathematical model of tumor growth, Mathe-
matical BioSciences, vol. 81, 1986, 229-244.
[2] J.A. Adam, A mathematical model of tumor growth II, effects of geometry
and spatial nonuniformity on stability, Mathematical BioSciences, vol 86,
1987, 183-211.
[3] A. Friedman, A hierarchy of cancer models and their mathematical chal-
lenges, Discrete and Continuous Dynamical systems, Series B, V4, no. 1,
2004.
496 L. Jaafar Belaid
[4] D. Grecu, A.S. Carstea, A.T. Grecu, A. Visinescu, Mathematical mod-
elling of tumor growth, Romanian Reports in Physics, vol. 59, no 2, 2007,
447-455.
[5] J.A. Sheratt, M.A.J. Chaplain, A new mathematical model for avascular
tumor growth, Math. Biol., vol 43, 2001, 291-312.
[6] A. Stephanou, S.R. McDougall, A.R.A. Anderson and M.A.J. Chaplain,
Mathematical modeling of flow in 2D and 3D vascular networks: appli-
cations to anti-angiogenic and chemotherapeutic drug strategies, Math.
Comp. Mod., vol 41, 2005, 1137-1156.
[7] Tiina Roose, S. Jonathan Chapman, Philip K Maini, Mathematical Mod-
els of Avascular Tumor Growth, Siam Review, vol 49, no. 2, 2007, 179-208.
[8] J.P Ward, J.R. King, Mathematical modelling of avascular tumor growth
I, IMA journal Math. Appl. Med. Biol., vol 14, no. 1, 1997, 39-69.
[9] J.P Ward, J.R. King, Mathematical modelling of avascular tumor growth
II: modelling growth saturation, IMA journal Math. Appl. Med. Biol, vol
15, 1998, 1-42.

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