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Applied Mathematics & Optimization

, Volume 72, Issue 3, pp 493–521 | Cite as

Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

  • Isaías Pereira de JesusEmail author
Article
First Online:
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Abstract

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the “follower players” (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results: the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg–Nash problem, where the optimality system for the leader is given.

Keywords

Micropolar fluids Stackelberg–Nash strategies Hierarchic control 

Mathematics Subject Classification

35K20 93B05 76D55 
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Notes

Acknowledgments

The author wants to express his gratitude to the anonymous reviewers for their questions and commentaries; they were very helpful in improving this article. The author also thanks Newton Santos for his comments on the manuscript.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Dpto. MatemáticaUniversidade Federal do PiauíTeresinaBrazil

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