An optimal control problem for a Kirchhoff-type equation
ESAIM: Control, Optimisation and Calculus of Variations, Volume 23 (2017) no. 3, pp. 773-790.

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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     title = {An optimal control problem for a {Kirchhoff-type} equation},
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     pages = {773--790},
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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, 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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