An approach for simultaneously determining the optimal trajectory and control of a cancerous model
الموضوعات :Hamid Reza Sahebi 1 , S. Ebrahimi 2
1 - Department of Mathematics, Islamic Azad University, Ashtian Branch,
Ashtian, Iran.
2 - Department of Mathematics, Islamic Azad University, Ashtian Branch,
Ashtian, Iran.
الکلمات المفتاحية: Optimal Trajectory, Cancerous Model,
ملخص المقالة :
The main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. There-fore we consider a control system governed by a bone marrow cancer equation.Next, by extending the underlying space, the existence of the solution is con-sidered and pair of the solution are identi ed simultaneously. In this mannera numerical example is also given.
[1] G. Chqquet, Lectures on Analysis, Benjamin, New York , 1969.
[2] R.E. Edwards,Functional Analysis Theory and Application, Holt, Rinehart
and Winston, New York, 1965.
[3] Fakharzadeh J., A. and J. E. Rubio, Global Solution of Optimal Shape
Designe Problems, ZAA Journal for Analysis and its Applications. 16,
(1999), 143-155.
[4] Rubio, J. E., Control and Optimization: the Linear Treatment of Non-
linear Problems, Manchester University Press, Manchester, (1986).
[5] Rubio, J. E., The Global Control of Non-linear Elliptic Equation, Journal
of Franklin Institute, 330(1), pp. 29-35, (1993).
[6] Rosenbloom, P. C., Qudques Classes de Problems Exteremaux, Bulltein de
Societe Mathematique de France, 80 , pp.183-216, (1952).
[7] A. Swierniak, A. Polanski, and M. Kimmel,Optimal control problems
arising in cell-cyclespeci c cancer chemotherapy, Cell Prolif., 29 , pp. 117-
139 (1996).
[8] G. W. Swan, Role of Optimal Control Theory in Cancer Chemotherapy,
Math. Biosci.,101, pp.237-284 (1990).
[9] H. Schattler, Optimal
controls for a model with pharmacokinetics maximizing bone marrow in
cancer chemotherapy,Mathematical Biosciences Volume 206, Issue 2,pp.
320-342 (2007).
[10] Xia, X,Modelling of bone marrow cancer. Vaccine readiness, drug
e ectiveness and therapeutical failures, Journal of Process Control. No
17.pp. 253-260 (2007).
[11] G.F. Webb, Resonance phenomena in cell population chemotherapy
models, Rocky Mountain J. of Mathematics., 20, pp. 1195-1216 (1990).
