Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions

Abstract

Abstract. 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 diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local optimality in an L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L ∞ .Mathematics Subject Classification. 49K20, 35J65, 80M50.

Unique solvability of a stationary radiative‐conductive heat transfer problem in a system consisting of an absolutely black body and several semitransparent bodies

“…The same field of studies comprises the solvability problems in radiation gas‐ and hydrodynamics 65–81 . We also mention works dealing with homogenization of radiative‐conductive heat exchange problems 82–92 and with optimal control in complex heat exchange problems 93–102 . Naturally, the above list of references is not complete.…”

State-Constrained Optimal Control of Semilinear Elliptic Equations with Nonlocal Radiation Interface Conditions

“…Based on the results of Laitinen and Tiihonen [12] for the nonlinear state equation, first-order necessary conditions for this problem are derived by Meyer, Philip, and Tröltzsch in [15]. Moreover, in [14], second-order sufficient conditions are established incorporating a generalized two-normdiscrepancy. However, these results cannot immediately be transfered to problem (P) due to the presence of pointwise state-constraints.…”