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This work represents a first contribution on the problem of boundarystabilization for the phase field system of Cahn-Hilliard type, which modelsthe phase separation in a binary mixture. The feedback controller we designhere is with actuation only on the temperature flow of the system, on one partof the boundary only. Moreover, it is of proportional type, given in anexplicit form, expressed only in terms of the eigenfunctions of the Laplaceoperator, being easy to manipulate from the computational point of view.Furthermore, it ensures that the closed loop nonlinear system exponentiallyreaches the prescribed stationary solution provided that the initial datum isclose enough to it.

Stabilization of a linearized Cahn-Hilliard system for phase separation by proportional boundary feedbacks