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.

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 L s -neighborhood of a reference function whereby the underlying analysis allows to use weaker norms than L .

DOI : 10.1051/cocv:2007028
Classification : 49K20, 35J65, 80M50
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] J. Bonnans, Second order analysis for control constrained optimal control problems of semilinear elliptic systems. Appl. Math. Optim. 38 (1998) 303-325. | Zbl

[2] H. Brezis, Analyse fonctionelle. Masson, Paris (1983). | MR | Zbl

[3] E. Casas and M. Mateos, 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] E. Casas, F. Tröltzsch and A. Unger, Second order sufficient optimality conditions for a nonlinear elliptic control problem. J. Anal. Appl. 15 (1996) 687-707. | Zbl

[5] A.L. Dontchev, W.W. Hager, A.B. Poore and B. Yang, Optimality, stability, and convergence in optimal control. Appl. Math. Optim. 31 (1995) 297-326. | Zbl

[6] O. Klein, P. Philip and J. Sprekels, Modeling and simulation of sublimation growth of SiC bulk single crystals. Interfaces Free Boundaries 6 (2004) 295-314. | Zbl

[7] M. Laitinen and T. Tiihonen, Conductive-radiative heat transfer in grey materials. Quart. Appl. Math. 59 (2001) 737-768.

[8] C. Meyer, P. Philip, and F. Tröltzsch, Optimal control of a semilinear PDE with nonlocal radiation interface conditions. SIAM J. Control Optim. 45 (2006) 699-721. | Zbl

[9] H.-J. Rost, D. Siche, J. Dolle, W. Eiserbeck, T. Müller, D. Schulz, G. Wagner and J. Wollweber, 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] T. Tiihonen, A nonlocal problem arising from heat radiation on non-convex surfaces. Eur. J. App. Math. 8 (1997) 403-416. | Zbl

[11] T. Tiihonen, Stefan-Boltzmann radiation on non-convex surfaces. Math. Meth. Appl. Sci. 20 (1997) 47-57. | Zbl

[12] F. Tröltzsch and D. Wachsmuth, Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: COCV 12 (2006) 93-119. | Numdam | Zbl

Cité par Sources :