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.

optimal control, tumor propagation, regional controllability, scalability.

Received: October 21, 2022; Revised: January 4, 2023; Accepted: January 5, 2023; Published: January 28, 2023

How to cite this article: Cheikh SECK, Mouhamadou NGOM and Lamine NDIAYE, A study on non-classical optimal control and dynamic regional controllability by scalability of tumor evolution, International Journal of Numerical Methods and Applications 23(1) (2023), 67-85. http://dx.doi.org/10.17654/0975045223004

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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