Geodesic
A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation
International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 3, pp. 409-418.

Voir la notice de l'article provenant de la source Library of Science

A lower and upper solution method is introduced for control problems related to abstract operator equations. The method is illustrated on a control problem for the Lotka-Volterra model with seasonal harvesting and applied to a control problem of cell evolution after bone marrow transplantation.
Keywords: control problem, lower and upper solution, fixed point, approximation algorithm, numerical solution, medical application
Mots-clés : sterowanie optymalne, punkt stały, algorytm aproksymacyjny, rozwiązanie numeryczne, zastosowanie medyczne 
@article{IJAMCS_2023_33_3_a4,
     author = {Parajdi, Lorand Gabriel and Precup, Radu and Haplea, Ioan \c{S}tefan},
     title = {A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation},
     journal = {International Journal of Applied Mathematics and Computer Science},
     pages = {409--418},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a4/}
}
TY  - JOUR
AU  - Parajdi, Lorand Gabriel
AU  - Precup, Radu
AU  - Haplea, Ioan Ştefan
TI  - A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation
JO  - International Journal of Applied Mathematics and Computer Science
PY  - 2023
SP  - 409
EP  - 418
VL  - 33
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a4/
LA  - en
ID  - IJAMCS_2023_33_3_a4
ER  - 
%0 Journal Article
%A Parajdi, Lorand Gabriel
%A Precup, Radu
%A Haplea, Ioan Ştefan
%T A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation
%J International Journal of Applied Mathematics and Computer Science
%D 2023
%P 409-418
%V 33
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a4/
%G en
%F IJAMCS_2023_33_3_a4
Parajdi, Lorand Gabriel; Precup, Radu; Haplea, Ioan Ştefan. A method of lower and upper solutions for control problems and application to a model of bone marrow transplantation. International Journal of Applied Mathematics and Computer Science, Tome 33 (2023) no. 3, pp. 409-418. http://geodesic.mathdoc.fr/item/IJAMCS_2023_33_3_a4/

[1] [1] Barbu, V. (2016). Differential Equations, Springer, Cham.

[2] [2] Coron, J.-M. (2007). Control and Nonlinearity, Mathematical Surveys and Monographs, Vol. 136, American Mathematical Society, Providence.

[3] [3] DeConde, R., Kim, P.S., Levy, D. and Lee, P.P. (2005). Post-transplantation dynamics of the immune response to chronic myelogenous leukemia, Journal of Theoretical Biology 236(1): 39-59.

[4] [4] Foley, C. and Mackey, M.C. (2009). Dynamic hematological disease: A review, Journal of Mathematical Biology 58(1): 285-322.

[5] [5] Haplea, I. ¸S., Parajdi, L.G. and Precup, R. (2021). On the controllability of a system modeling cell dynamics related to leukemia, Symmetry 13(10): 1867.

[6] [6] Kelley, C.T. (1995). Iterative Methods for Linear and Nonlinear Equations, SIAM, Philadelphia.

[7] [7] Kim, P.S., Lee, P.P. and Levy, D. (2007). Mini-transplants for chronic myelogenous leukemia: A modeling perspective, in I. Queinnec (Ed.), Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences, Vol. 357, Springer, Berlin, pp. 3-20.

[8] [8] Langtangen, H.P. and Mardal, K.A. (2019). Introduction to Numerical Methods for Variational Problems, Springer, Cham.

[9] [9] Parajdi, L.G. (2020). Stability of the equilibria of a dynamic system modeling stem cell transplantation, Ricerche di Matematica 69(2): 579-601.

[10] [10] Parajdi, L.G., Patrulescu, F.-O., Precup, R. and Haplea, I.Ş. (2023). Two numerical methods for solving a nonlinear system of integral equations of mixed Volterra-Fredholm type arising from a control problem related to leukemia, Journal of Applied Analysis & Computation, DOI: 10.11948/20220197, (online first).

[11] [11] Precup, R. (2002). Methods in Nonlinear Integral Equations, Kluwer Academic Publishers, Dordrecht.

[12] [12] Precup, R. (2022). On some applications of the controllability principle for fixed point equations, Results in Applied Mathematics 13: 100236.

[13] [13] Precup, R., Dima, D., Tomuleasa, C., ¸Serban, M.-A. and Parajdi, L.-G. (2018). Theoretical models of hematopoietic cell dynamics related to bone marrow transplantation, in Atta-ur-Rahman and S. Anjum (Eds.), Frontiers in Stem Cell and Regenerative Medicine Research,Vol. 8, Bentham Science Publishers, Sharjah, pp. 202-241.

[14] [14] Precup, R., Şerban, M.-A. and Trif, D. (2013). Asymptotic stability for a model of cell dynamics after allogeneic bone marrow transplantation, Nonlinear Dynamics and Systems Theory 13(1): 79-92.

[15] [15] Precup, R., Şerban, M.-A., Trif, D. and Cucuianu, A. (2012). A planning algorithm for correction therapies after allogeneic stem cell transplantation, Journal of Mathematical Modelling and Algorithms 11(3): 309-323.

[16] [16] Precup, R., Trif, D., Şerban, M.-A. and Cucuianu, A. (2010). A mathematical approach to cell dynamics before and after allogeneic bone marrow transplantation, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity 8: 167-175.

[17] [17] Rahmani Doust, M.H. (2015). The efficiency of harvested factor: Lotka-Volterra predator-prey model, Caspian Journal of Mathematical Sciences 4(1): 51-59.