WIAS Preprint No. 976, (2004)

Optimal control of a semilinear PDE with nonlocal radiation interface conditions


  • Meyer, Christian
  • Philip, Peter
  • Tröltzsch, Fredi

2010 Mathematics Subject Classification

  • 49K20 35J65 49J20 80M50


  • Optimal control, semilinear elliptic equations, nonlocal interface conditions, boundedness of solutions


We consider a control 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 problem arises from the aim to optimize the temperature gradient within crystal growth by the physical vapor transport (PVT) method. Based on a minimum principle for the semilinear equation as well as L-infinity estimates for the weak solution, we establish the existence of an optimal solution as well as necessary optimality conditions. The theoretical results are illustrated by results of numerical computations.

Appeared in

  • SIAM Journal On Control and Optimization 45 (2006), pp.699-721.

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