Abstract
In this paper, we consider a distributed optimal control problem for the new mechanochemical model in biological patterns which was proposed to describe the dynamics of basal lamina, dermal and epidermal tissues. The model consists of the time-dependent Ginzburg-Landau equation for the concentration difference of at least two pigments ϕ coupled with the Swift-Hohenberg equation for the difference of dermal cellular densities of at least two types of cells ψ. First we prove the existence and uniqueness of a strong solution. The existence of optimal controls is established. Then we prove the control-to-state operator S is Fréchet differentiable. Finally we derive the first-order necessary optimality conditions for the optimal control problem.
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