Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Doi
Abstract
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 L2-neighborhood