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Licensed Unlicensed Requires Authentication Published by De Gruyter 2022

13 Feedback stabilization of Cahn–Hilliard phase-field systems

From the book Optimization and Control for Partial Differential Equations

  • Gabriela Marinoschi


We provide a compact presentation, relying on the papers [4, 17, 18], of the internal feedback stabilization of phase-field systems of Cahn-Hilliard type by using a feedback controller with support in a subset of the flow domain. Here the feedback stabilization technique is based on the design of the controller as a linear combination of the unstable modes of the corresponding linearized system, followed by its representation in a feedback form by means of an optimization method. Results are provided both for a regular potential involved in the phase field equation (the doublewell potential) and for a singular case represented by a logarithmic-type potential. The feedback stabilization is studied in the case with viscosity effects and in the limit case as the viscosity tends to zero.

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