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Research Article | Open Access

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

Monica Conti1, Stefania Gatti2, Alain Miranville3,4( )
Politecnico di Milano, Dipartimento di Matematica "F. Brioschi", Via Bonardi 9, I-20133 Milano, Italy
Università di Modena e Reggio Emilia, Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Via Campi 213/B, I-41125 Modena, Italy
Xiamen University, School of Mathematical Sciences, Xiamen, Fujian, China
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
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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.

Keywords

brain cancerchemiotherapyantiangiogenic therapywell-posednessoptimal control
CLC number: 35B50, 35D30, 35Q92, 92C50

References

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1536-1561
DOI: 10.3934/math.2022090

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Conti M, Gatti S, Miranville A. Mathematical analysis of a phase-field model of brain cancers with chemotherapy and antiangiogenic therapy effects. AIMS Mathematics, 2022, 7(1): 1536-1561. https://doi.org/10.3934/math.2022090

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Received: 22 October 2021
Accepted: 27 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)