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A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions

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Abstract

A boundary control problem for the viscous Cahn–Hilliard equations with possibly singular potentials and dynamic boundary conditions is studied and first order necessary conditions for optimality are proved.

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Acknowledgments

Some financial support from the MIUR-PRIN Grant 2010A2TFX2 “Calculus of variations” and the GNAMPA (Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica) is gratefully acknowledged by PC and GG.

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Authors and Affiliations

  1. Dipartimento di Matematica “F. Casorati”, Universitá di Pavia and Research Associate at the IMATI – C.N.R. PAVIA, via Ferrata 1, 27100, Pavia, Italy

    Pierluigi Colli & Gianni Gilardi

  2. Weierstrass Institute, Mohrenstrasse 39, 10117, Berlin, Germany

    Jürgen Sprekels

  3. Department of Mathematics, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Jürgen Sprekels

Authors
  1. Pierluigi Colli
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  2. Gianni Gilardi
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  3. Jürgen Sprekels
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Correspondence to Jürgen Sprekels.

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Colli, P., Gilardi, G. & Sprekels, J. A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions. Appl Math Optim 73, 195–225 (2016). https://doi.org/10.1007/s00245-015-9299-z

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