[1] S.Amstutz Aspects th´eoriques et num´eriques en optimisation de forme
topologique, Th`ese , INSA Toulouse 2003.
[2] B.V.Bazaly and A.Friedman A Free Boundary Probleme for an Elliptic-
Parabolic System : Application to a Model of Tumor Growth Communication
in Partial Differential Equations Vol. 28 Nos 3 and 4, pp. 517-560,
2003
[3] B.Bazaly et A.Friedman Global Existence and Asymptotic Stability for An
Elliptic-parabolique Free Boundary Prolem :
An Application to a model of Tumor Growth. Indiana University Mathematics
Journal, Vol.52, No.5 (2003)
[4] M.A.J. Chaplain The development of a spatial pattern in a model for cancer
growth, Experimental and Theoretical Advances in Biological Pattern
Formation (H. G. Othmer, P. K. Maini, and J. D. Murray, eds.), Plenum
Press, 1993, pp. 45-60.
[5] S Cui, A Friedman Analysis of a mathematical of the effect inhibitors on
the growth of tumors. Mathematical Biosciences 164 (2000) 103-137
[6] S.Cui and A.Friedman Analysis of a mathematical model of the growth of
necrotic tumors Journal of Mathematical Analysis and Applications 255,
636-677 (2001)
[7] S.Cui and A.Friedman A Free Boundary Problme For A Singular System
Of Differential Equations : An Application To A Model Of Tumor
Growth0.Transactions of the American Mathematical Society. Vol.355,
Number 9, p.3537-3590 (2003)
[8] R. Dautray. J.L. Lions. Analyse math´ematique et calcul num´erique pour
les sciences et techniques. Tome II, Masson, Paris 1987.
[9] De Pillis,L.G and Radunskaya,A., A mathematical tumor model with immune
resistance and drug therapy: an optimal control approach, Journal
of Theoretical Medicine, 2000
[10] A.Friedman Free boundary problems arising in tumor models Mat. Acc.
Lincei (2004) s.9, v.15 : 161-168
Chemotherapy of a tumor by optimal control approach 801
[11] A.Friedman and F.Reitich Analysis of a mathematical model for the
growth of tumors J. Math. Biol. (1999) 38: 262-284
[12] A.Friedman and F.Reitich Symmetry-Breaking Bifurcation of Analytic solutions
to Free Boundary Problems : An Application to A Model of Tumor
Growth.Transactions of the American Mathematical Society. Vol. 353,
Number 4, Pages 1587-1634, (2000) Springer-Verlag 1994
[13] S. Garreau, Ph Guillaume and M. Masmoudi, The topological asymptotic
for PDE systems: the elastic case. SIAM Control and optim. 39(6) pp
1756-1778, 2001.
[14] H.P. Greenspan Models for the growth of a solid tumor by diffusion, Studies
Appl. Math. 52 (1972), 317-340
[15] H.P. Greenspan On the growth on cell culture and solid tumors, Theoretical
Biology 56 (1976), 229-242
[16] Ph. Guillaume and M. Masmoudi Computation of high order derivatices
in optimal design Numerische Mathematik pp 213-250
[17] Ph. Guillaume and K. Sid Idris: The topological expansion for the Dirichlet
problem, SIAM J. Control and optim. 41(4), pp 1042-1072, 2002.
[18] Kimmel,M. and Swierniak,A. Control Theory Approach to Cancer
Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug
Resistance,
[19] Ledzewicz,U., and Sachattlerl,H., Drug resistance in cancer chemotherapy
as an optimal control problem, Discrete and continuous dynamical
systems- series-B Volume 6, Number 1, January 2006,pp. 129-150
[20] F.L.Levis, V.L.Syrmos Optimal control2nd Edition Hardcover Paperback
1995
[21] J.L.Lions Contrˆole optimal des syst`eme distribu´es gouvern´es par des Equations
aux D´eriv´ees Partielles, DUNOD 1968
[22] M. Masmoudi, The topological asymptotic, in computational methods for
control applications, H. Kawarada and J. Periaux, eds, GAKUTO Internat.
Ser. Math. Sci. Appli. Gakkot¯osho, Tokyo, 2002.
[23] S.A. Nazarov, J. Sokolowski Asyptotic analysys of Shape Functionnals J Math.
Pures Appl. 82 (2003) pp 125-196.
[24] M.Ngom, I.Ly and D.Seck Study of a tumor by shape and topological optimiza-
tion. Applied Mathematical Sciences, Vol. 5, 2011, no. 1, 1-21
802 Ngom, Ly and Seck
[25] Y.Renard+,J.Pommier GETFEM++ An open source generic C++ library for
nit element methods, http://home.gna.org/getfem/.
[26] Swan ,G. W. Role of optimal control theory in cancer chemotherapy, Math
Biosci. 1990 Oct;101(2):237-84
[27] Swan ,G. W. Optimal Control Analysis of a Cancer Chemotherapy Problem,
Mathematical Medicine and Biology 1987 4(2):171-184
Thank you for copying data from http://www.arastirmax.com