Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs

Hawraa Alsayed; Hussein Fakih; Alain Miranville; Ali Wehbe

doi:10.3934/dcdss.2022003

Article Contents

2022, Volume 15, Issue 12: 3481-3515. Doi: 10.3934/dcdss.2022003

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Optimal control of an Allen-Cahn model for tumor growth through supply of cytotoxic drugs

1.
Université de Poitiers, Laboratoire de Mathématiques et Applications, UMR CNRS 7348 - SP2MI, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France
2.
Lebanese University, Khawarizmi Laboratory for Mathematics and Applications, Beirut, Lebanon
3.
Lebanese International University, Department of Mathematics and Physics, Lebanon
4.
Xiamen University, School of Mathematical Sciences, Xiamen, Fujian, China
5.
Université de Poitiers, Laboratoire I3M and Laboratoire de Mathématiques et Applications, Boulevard Marie et Pierre Curie - Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

^*Corresponding author: Alain Miranville
^*Corresponding author: Alain Miranville

Received: August 2021

Revised: November 2021

Early access: January 2022

Published: December 2022

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Abstract

Our aim in this paper is to study an optimal control problem for a tumor growth model. The state system couples an Allen-Cahn equation and a reaction diffusion equation that models the evolution of tumor in the presence of nutrient supply. Elimination of cancer cells via cytotoxic drug is considered and the concentration of the cytotoxic drug is represented as a control variable.

Keywords:

Glioma treatment,
Allen-Cahn equation,
cytotoxic drugs,
first order necessary optimality conditions.

Mathematics Subject Classification: 35Q93, 35K20, 49K20, 49J20, 92C50.

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