Geodesic
An optimal control problem for a Kirchhoff-type equation
Delgado, M.1 ; Figueiredo, G. M.2 ; Gayte, I.1 ; Morales-Rodrigo, C.1
1 Departement de Ecuaciones Diferenciales y Análisis Numérico, Faculdade de Matemáticas, Universidade de Sevilla Calle Tarfia s/n, 41012 Sevilla, Spain.
2 Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, 66.075-110 Belém-Pará, Brazil.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 3, pp. 773-790.

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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.

DOI : 10.1051/cocv/2016013
Classification : 47J05, 49J20, 49J22, 49K20
Keywords: Optimal control, optimality system, adjoint problem, Euler–Lagrange equation, Kirchhoff equation

Delgado, M. 1 ; Figueiredo, G. M. 2 ; Gayte, I. 1 ; Morales-Rodrigo, C. 1

1 Departement de Ecuaciones Diferenciales y Análisis Numérico, Faculdade de Matemáticas, Universidade de Sevilla Calle Tarfia s/n, 41012 Sevilla, Spain.
2 Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, 66.075-110 Belém-Pará, Brazil. 
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     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},
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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, Tome 23 (2017) no. 3, pp. 773-790. doi : 10.1051/cocv/2016013. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2016013/

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