A STUDY ON NON-CLASSICAL OPTIMAL CONTROL AND DYNAMIC REGIONAL CONTROLLABILITY BY SCALABILITY OF TUMOR EVOLUTION
Keywords:
optimal control, tumor propagation, regional controllability, scalabilityDOI:
https://doi.org/10.17654/0975045223004Abstract
In this paper, we are interested in Cauchy problem for a parabolic operator. The main system comes from the modeling of a tumor and describes its evolution over time. From the classical optimal control, we show some results and an optimality system for the considered control problem. It is noteworthy that the classical techniques of the optimal control theory are ineffective or are very much technical for certain systems of parabolic evolution. Thus, we address regional controllability by scalability to get around certain difficulties related to estimations. Starting from the solution of the obtained optimality system, we succeeded in establishing the controllability on dynamic subdomains by area-leveling to solve the optimal control problem for this kind of equations.
Received: October 21, 2022
Revised: January 4, 2023
Accepted: January 5, 2023
References
H. P. Greenspan, Models for the growth of a solid tumor by diffusion, Studies Appl. Math. 52 (1972), 317-340.
H. P. Greenspan, On the growth on cell culture and solid tumors, Theoretical Biology 56 (1976), 229-242.
M. Kimmel and A. Swierniak, Control Theory Approach to Cancer Chemotherapy: Benefiting from Phase Dependence and Overcoming Drug Resistance, Lect. Notes Math. 1872 (2006), pp. 185-221.
U. Ledzewicz and H. Sachattlerl, Drug resistance in cancer chemotherapy as an optimal control problem, Discrete and Continuous Dynamical Systems- Series-B 6(1) (2006), 129-150.
M. Ngom, I. Ly and D. Seck, Study of a tumor by shape and topological optimization, Applied Mathematical Sciences 5(1) (2011), 1-21.
A. Friedman, Free boundary problems arising in tumor models, Mat. Acc. Lincei 15(9) (2004), 161-168.
S. Cui and A. Friedman, Analysis of a mathematical of the effect inhibitors on the growth of tumors, Mathematical Biosciences 164 (2000), 103-137.
S. Cui and A. Friedman, Analysis of a mathematical model of the growth of necrotic tumors, Journal of Mathematical Analysis and Applications 255 (2001), 636-677.
G. 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.
A. El Jai and A. J. Pritchard, Distributed parameter systems analysis via sensors and actuators, J. Wiley, Texts in Appl. Math. (1988).
J. L. Lions, Contrôle à moindres regrets des systèmes distribués, C. R. Acad. Sci. Paris, Ser. I Math. 315 (1992), 1253-1257.
J. L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome 1, Research in Applied Mathematics, Volume 8, Perturbations, Masson, Paris, 1988.
J. L. Lions, Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués, Tome 2, Research in Applied Mathematics, Volume 8, Perturbations, Masson, Paris, 1988.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 International Journal of Numerical Methods and Applications
This work is licensed under a Creative Commons Attribution 4.0 International License.
Attribution: Credit Pushpa Publishing House as the original publisher, including title and author(s) if applicable.
Non-Commercial Use: For non-commercial purposes only. No commercial activities without explicit permission.
No Derivatives: Modifying or creating derivative works not allowed without written permission.
Contact Pushpa Publishing House for more info or permissions.
Publication count: 
Citation count: 
Google h-index: 
Downloads: 