WIAS Preprint No. 1234, (2007)

State-constrained optimal control of semilinear elliptic equations with nonlocal radiation interface conditions


  • Meyer, Christian
  • Yousept, Irwin

2010 Mathematics Subject Classification

  • 35J60 49K20 49M05 65K10


  • Nonlinear optimal control, nonlocal radiation interface conditions, state constraints, first-order necessary conditions, second-order sufficient conditions


We consider a control- and state-constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffuse-gray conductive-radiative heat transfer. The nonlocal radiation interface condition and the pointwise state-constraints represent the particular features of this problem. To deal with the state-constraints, continuity of the state is shown which allows to derive first-order necessary conditions. Afterwards, we establish second-order sufficient conditions that account for strongly active sets and ensure local optimality in an $L^2$-neighborhood.

Appeared in

  • SIAM J. Control Optim., 48 (2009) pp. 734--755

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