Optimal control of a semilinear PDE with nonlocal radiation interface conditions. (English) Zbl 1109.49026

Meyer, C.; Philip, P.; Tröltzsch, F.

SIAM J. Control Optim. 45, No. 2, 699-721 (2006).

Summary: 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 when attempting 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 \(L^\infty\)-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 numerical computations.

MSC:

49K20	Optimality conditions for problems involving partial differential equations
35J65	Nonlinear boundary value problems for linear elliptic equations
49J20	Existence theories for optimal control problems involving partial differential equations
80M50	Optimization problems in thermodynamics and heat transfer

Keywords:

optimal control; semilinear elliptic equations; nonlocal interface conditions; boundedness of solutions