Stability analysis on a hybrid PDE-ODE system describing intermittent hormonal therapy of prostate cancer

Kurumi Hiruko; Shinya Okabe

doi:10.1142/S0218202518500136

Stability analysis on a hybrid PDE-ODE system describing intermittent hormonal therapy of prostate cancer

Kurumi Hiruko, Shinya Okabe

SCI - Mathematics

Tohoku University

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider the stability of control prescribed by hybrid PDE-ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE-ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.

Original language	English
Pages (from-to)	487-523
Number of pages	37
Journal	Mathematical Models and Methods in Applied Sciences
Volume	28
Issue number	3
DOIs	https://doi.org/10.1142/S0218202518500136
Publication status	Published - 2018 Mar 1

Keywords

Comparison principle
energy method
indirectly controlled parameter

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10.1142/S0218202518500136

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abstract = "We consider the stability of control prescribed by hybrid PDE-ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE-ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.",

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AU - Okabe, Shinya

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N2 - We consider the stability of control prescribed by hybrid PDE-ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE-ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.

AB - We consider the stability of control prescribed by hybrid PDE-ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE-ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.

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KW - energy method

KW - indirectly controlled parameter

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Stability analysis on a hybrid PDE-ODE system describing intermittent hormonal therapy of prostate cancer

Abstract

Keywords

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