Hierarchic Control for the Wave Equation

  • Fágner Dias ArarunaEmail author
  • Enrique Fernández-Cara
  • Luciano Cipriano da Silva


This paper deals with the hierarchical control of the wave equation. We use Stackelberg–Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we look for a leader that solves an exact controllability problem. We consider linear and semilinear equations.


Wave equation Exact controllability Stackelberg–Nash strategy Carleman inequalities 

Mathematics Subject Classification

35L05 90C29 93B05 



Fágner Dias Araruna has been partially supported by INCTMat, CAPES, CNPq (Brazil), and MathAmSud COSIP. Enrique Fernández-Cara has been partially supported by Grant MTM2016-76990-P (DGI-MICINN, Spain) and CAPES (Brazil). Luciano Cipriano da Silva has been partially supported by CAPES (Brazil).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dpto. de MatemáticaUniversidade Federal da ParaíbaJoão PessoaBrazil
  2. 2.Dpto. EDAN and IMUSUniversidad de SevillaSevillaSpain

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