Abstract
This paper deals with a chemotaxis–haptotaxis model which described the process of cancer invasion on the macroscopic scale. We first explore the global-in-time existence and uniqueness of a strong solution. For a class of cost functionals, we prove first-order necessary optimality conditions for the corresponding optimal control problem and establish the existence of Lagrange multipliers. Finally, we derive some extra regularity for the Lagrange multiplier.
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