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Existence, Stability and Optimal Drug Dosage for a Reaction-Diffusion System Arising in a Cancer Treatment by Morgan, Jeff; Tang, Bao Quoc; Yin, Hong-Ming is a scholarly article available to read on EtoBox.

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In this paper, a reaction-diffusion system modeling injection of a chemotherapeutic drug on the surface of a living tissue during a treatment for cancer patients is studied. The system describes the interaction of the chemotherapeutic drug and the normal, tumor and immune cells. We first establish well-posedness for the nonlinear reaction-diffusion system, then investigate the long-time behavior of solutions. Particularly, it is shown that the cancer cells will be eliminated assuming that its reproduction rate is sufficiently small in a short time period in each treatment interval. The analysis is then essentially exploited to study an optimal drug injection rate problem during a chemotherapeutic drug treatment for tumor cells, which is formulated as an optimal boundary control problem with constraints. For this, we show that the existence of an optimal drug injection rate through the boundary, and derive the first-order optimality condition.

Author

Morgan, Jeff; Tang, Bao Quoc; Yin, Hong-Ming

Published

2024

Language

EN