Author(s) :
Christian Meyer
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 13-2005
MSC 2000
- 49K20 Problems involving partial differential equations
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35J65 Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
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 diffuse-gray 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 a $L^s$-neighborhood whereby the underlying analysis allows to use weaker norms than $L^\infty$.
Keywords :
Optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions