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