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Controllability of hybrid PDE‐ODE systems with structural instability and applications to mathematical models on intermittent hormonal therapy for prostate cancer
Author(s) -
Hiruko Kurumi,
Okabe Shinya
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5284
Subject(s) - ode , controllability , prostate cancer , mathematics , instability , hormonal therapy , cancer , medicine , physics , mechanics
Several mathematical models on intermittent androgen suppression (IAS) therapy for prostate cancer are classified into hybrid PDE‐ODE system with structural instability. The purpose of this paper is to give a unified strategy to prove the controllability of the mathematical models on the IAS therapy. For this aim, we prove that (1) a generalized hybrid PDE‐ODE system is controllable for any initial data and (2) the result given by (1) is applicable to the mathematical models on the IAS therapy. Finally, we conclude that the mathematical models on the IAS therapy for prostate cancer are controllable for any initial data.