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We investigate a nonstandard phase field model of Cahn-Hilliard type. Themodel describes two-species phase segregation and consists of a system of twohighly nonlinearly coupled PDEs. It has been studied recently in the papersarXiv:1103.4585 and arXiv:1109.3303 for the case of homogeneous Neumannboundary conditions. In this paper, we investigate the case that the boundarycondition for one of the unknowns of the system is of third kind andnonhomogeneous. For the resulting system, we show well-posedness, and we studyoptimal boundary control problems. Existence of optimal controls is shown, andthe first-order necessary optimality conditions are derived. Owing to thestrong nonlinear couplings in the PDE system, standard arguments of optimalcontrol theory do not apply directly, although the control constraints and thecost functional will be of standard type.

Analysis and optimal boundary control of a nonstandard system of phase field equations