In this paper we study a control problem for a Kirchhoff-type equation. The method to obtain first order necessary optimality conditions is the Dubovitskii–Milyoutin formalism because the classical arguments do not work. We obtain a characterization of the optimal control by a partial differential system which is solved numerically.
Keywords: Optimal control, optimality system, adjoint problem, Euler–Lagrange equation, Kirchhoff equation
@article{COCV_2017__23_3_773_0, author = {Delgado, M. and Figueiredo, G. M. and Gayte, I. and Morales-Rodrigo, C.}, title = {An optimal control problem for a {Kirchhoff-type} equation}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {773--790}, publisher = {EDP-Sciences}, volume = {23}, number = {3}, year = {2017}, doi = {10.1051/cocv/2016013}, mrnumber = {3660448}, zbl = {06736464}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016013/} }
TY - JOUR AU - Delgado, M. AU - Figueiredo, G. M. AU - Gayte, I. AU - Morales-Rodrigo, C. TI - An optimal control problem for a Kirchhoff-type equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2017 SP - 773 EP - 790 VL - 23 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016013/ DO - 10.1051/cocv/2016013 LA - en ID - COCV_2017__23_3_773_0 ER -
%0 Journal Article %A Delgado, M. %A Figueiredo, G. M. %A Gayte, I. %A Morales-Rodrigo, C. %T An optimal control problem for a Kirchhoff-type equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2017 %P 773-790 %V 23 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016013/ %R 10.1051/cocv/2016013 %G en %F COCV_2017__23_3_773_0
Delgado, M.; Figueiredo, G. M.; Gayte, I.; Morales-Rodrigo, C. An optimal control problem for a Kirchhoff-type equation. ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 3, pp. 773-790. doi : 10.1051/cocv/2016013. http://archive.numdam.org/articles/10.1051/cocv/2016013/
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