TY - GEN A1 - Colli, Pierluigi A1 - Gilardi, Gianni A1 - Sprekels, Jürgen T1 - Analysis and optimal boundary control of a nonstandard system of phase field equations N2 - We investigate a nonstandard phase field model of Cahn-Hilliard type. The model, which was introduced in [16], describes two-species phase segregation and consists of a system of two highly nonlinearly coupled PDEs. It has been studied recently in [5], [6] for the case of homogeneous Neumann boundary conditions. In this paper, we investigate the case that the boundary condition for one of the unknowns of the system is of third kind and nonhomogeneous. For the resulting system, we show well-posedness, and we study optimal boundary control problems. Existence of optimal controls is shown, and the first-order necessary optimality conditions are derived. Owing to the strong nonlinear couplings in the PDE system, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional will be of standard type. KW - nonlinear phase field systems KW - Cahn--Hilliard systems KW - parabolic systems KW - optimal boundary control KW - first-order necessary optimality conditions Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1066 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-10665 ER -