Abstract
We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations, 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 three 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.
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Acknowledgments
The authors want to express their gratitude to the anonymous reviewers for their questions and commentaries; they were very helpful in improving this article. F. D. Araruna’s work was partially supported by INCTMat, CAPES, CNPq (Brazil). M. A. Rojas-Medar’s work was partially supported by project Fondecyt (Chile) by Grant 1120260 and Ministerio de Ciencia e Tecnologa (Spain) by Grant MTM2012-32325.
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Araruna, F.D., de Menezes, S.D.B. & Rojas-Medar, M.A. On the Approximate Controllability of Stackelberg–Nash Strategies for Linearized Micropolar Fluids. Appl Math Optim 70, 373–393 (2014). https://doi.org/10.1007/s00245-014-9240-x
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DOI: https://doi.org/10.1007/s00245-014-9240-x