WIAS Preprint No. 2032, (2014)

Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition


Authors

  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Farshbaf Shaker, Mohammad Hassan
    ORCID: 0000-0003-0543-5938
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 35K55 35K50 82C26

Keywords

  • Cahn--Hilliard equation, dynamic boundary conditions, phase separation, singular potentials, optimal control, first and second order optimality conditions, adjoint state system

DOI

10.20347/WIAS.PREPRINT.2032

Abstract

In this paper we establish second-order sufficient optimality conditions for a boundary control problem that has been introduced and studied by three of the authors in the preprint arXiv:1407.3916. This control problem regards the viscous Cahn--Hilliard equation with possibly singular potentials and dynamic boundary conditions.

Appeared in

  • Ann. Acad. Rom. Sci. Math. Appl., 7 (2015) pp. 41--66 .

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