| Issue |
ESAIM: COCV
Volume 23, Number 3, July-September 2017
|
|
|---|---|---|
| Page(s) | 773 - 790 | |
| DOI | https://doi.org/10.1051/cocv/2016013 | |
| Published online | 29 March 2017 | |
An optimal control problem for a Kirchhoff-type equation
1 Departement de Ecuaciones Diferenciales y Análisis Numérico, Faculdade de Matemáticas, Universidade de Sevilla Calle Tarfia s/n, 41012 Sevilla, Spain.
madelgado@us.es; gayte@us.es; cristianm@us.es
2 Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, 66. 075-110 Belém-Pará, Brazil.
giovany@ufpa.br
Received: 1 October 2014
Revised: 8 August 2015
Accepted: 2 March 2016
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.
Mathematics Subject Classification: 47J05 / 49J20 / 49J22 / 49K20
Key words: Optimal control / optimality system / adjoint problem / Euler–Lagrange equation / Kirchhoff equation
© EDP Sciences, SMAI 2017
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