Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects

Monica Conti; Stefania Gatti; Alain Miranville; Monica Conti; Stefania Gatti; Alain Miranville

doi:10.3934/math.2022090

AIMS Mathematics

2022, Volume 7, Issue 1: 1536-1561. doi: 10.3934/math.2022090

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Research article

Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects

1.
Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, I-20133 Milano, Italy
2.
Università di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Via Campi 213/B, I-41125 Modena, Italy
3.
Xiamen University, School of Mathematical Sciences, Xiamen, Fujian, China
4.
Université de Poitiers, Laboratoire I3M et Laboratoire de Mathématiques et Applications, Equipe DACTIM-MIS, SP2MI, Boulevard Marie et Pierre Curie, Téléport 2, F-86962 Chasseneuil Futuroscope Cedex, France

Received: 22 October 2021 Accepted: 27 October 2021 Published: 28 October 2021
MSC : 35B50, 35D30, 35Q92, 92C50

Our aim in this paper is to study a mathematical model for brain cancers with chemotherapy and antiangiogenic therapy effects. We prove the existence and uniqueness of biologically relevant (nonnegative) solutions. We then address the important question of optimal treatment. More precisely, we study the problem of finding the controls that provide the optimal cytotoxic and antiangiogenic effects to treat the cancer.
- brain cancer,
- chemiotherapy,
- antiangiogenic therapy,
- well-posedness,
- optimal control
Citation: Monica Conti, Stefania Gatti, Alain Miranville. Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects[J]. AIMS Mathematics, 2022, 7(1): 1536-1561. doi: 10.3934/math.2022090

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Abstract

Our aim in this paper is to study a mathematical model for brain cancers with chemotherapy and antiangiogenic therapy effects. We prove the existence and uniqueness of biologically relevant (nonnegative) solutions. We then address the important question of optimal treatment. More precisely, we study the problem of finding the controls that provide the optimal cytotoxic and antiangiogenic effects to treat the cancer.

References

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