WIAS Preprint No. 1630, (2011)

Distributed optimal control of a nonstandard system of phase field equations


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Gilardi, Gianni
    ORCID: 0000-0002-0651-4307
  • Podio-Guidugli, Paolo
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 74A15 35K55 49K20


  • distributed optimal control, nonlinear phase field systems, first-order necessary optimality conditions




We investigate a distributed optimal control problem for a phase field model of Cahn-Hilliard type. The model describes two-species phase segregation on an atomic lattice under the presence of diffusion; it has been introduced recently in [4], on the basis of the theory developed in [15], and consists of a system of two highly nonlinearly coupled PDEs. For this reason, standard arguments of optimal control theory do not apply directly, although the control constraints and the cost functional are of standard type. We show that the problem admits a solution, and we derive the first-order necessary conditions of optimality.

Appeared in

  • Contin. Mech. Thermodyn., 24 (2012) pp. 437--459.

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