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 an -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than .
Mots-clés : optimal control, semilinear elliptic equations, nonlocal interface conditions, second-order sufficient optimality conditions
@article{COCV_2007__13_4_750_0,
author = {Meyer, Christian},
title = {Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {750--775},
publisher = {EDP-Sciences},
volume = {13},
number = {4},
year = {2007},
doi = {10.1051/cocv:2007028},
mrnumber = {2351402},
zbl = {1127.49020},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007028/}
}
TY - JOUR AU - Meyer, Christian TI - Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2007 SP - 750 EP - 775 VL - 13 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007028/ DO - 10.1051/cocv:2007028 LA - en ID - COCV_2007__13_4_750_0 ER -
%0 Journal Article %A Meyer, Christian %T Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions %J ESAIM: Control, Optimisation and Calculus of Variations %D 2007 %P 750-775 %V 13 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2007028/ %R 10.1051/cocv:2007028 %G en %F COCV_2007__13_4_750_0
Meyer, Christian. Second-order sufficient optimality conditions for a semilinear optimal control problem with nonlocal radiation interface conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 4, pp. 750-775. doi : 10.1051/cocv:2007028. http://www.numdam.org/articles/10.1051/cocv:2007028/
[1] , Second order analysis for control constrained optimal control problems of semilinear elliptic systems. Appl. Math. Optim. 38 (1998) 303-325. | Zbl
[2] , Analyse fonctionelle. Masson, Paris (1983). | MR | Zbl
[3] and, Second order sufficient optimality conditions for semilinear elliptic control problems with finitely many state constraints. SIAM J. Control Optim. 40 (2002) 1431-1454. | Zbl
[4] , and, Second order sufficient optimality conditions for a nonlinear elliptic control problem. J. Anal. Appl. 15 (1996) 687-707. | Zbl
[5] ,, and, Optimality, stability, and convergence in optimal control. Appl. Math. Optim. 31 (1995) 297-326. | Zbl
[6] , and, Modeling and simulation of sublimation growth of SiC bulk single crystals. Interfaces Free Boundaries 6 (2004) 295-314. | Zbl
[7] and, Conductive-radiative heat transfer in grey materials. Quart. Appl. Math. 59 (2001) 737-768.
[8] ,, and, Optimal control of a semilinear PDE with nonlocal radiation interface conditions. SIAM J. Control Optim. 45 (2006) 699-721. | Zbl
[9] ,,,,,, and, Influence of different growth parameters and related conditions on 6H-SiC crystals grown by the modified Lely method. Mater. Sci. Eng. B 61-62 (1999) 68-72.
[10] , A nonlocal problem arising from heat radiation on non-convex surfaces. Eur. J. App. Math. 8 (1997) 403-416. | Zbl
[11] , Stefan-Boltzmann radiation on non-convex surfaces. Math. Meth. Appl. Sci. 20 (1997) 47-57. | Zbl
[12] and, Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: COCV 12 (2006) 93-119. | Numdam | Zbl
Cité par Sources :
