Abstract
In this work, we study an advection---reaction---diffusion system involving normal and cancer hematopoietic cells (HC) and modeling the development of leukemia in the bone marrow. The effects of a targeted cytostatic therapy, which inhibits the regeneration of cancer HC, are studied through an optimal control system. We prove the existence of a positive bounded solution and the existence of an optimal controls by semigroup techniques. Conditions of optimality are in terms of the dual system. The effects of targeted cytostatic therapy, upon the dynamics of normal and cancer HC, are discussed through numerical simulations.
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