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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the approximate controllability of Stackelberg-Nash strategies for Stokes equations


Authors: F. Guillén-González, F. Marques-Lopes and M. Rojas-Medar
Journal: Proc. Amer. Math. Soc. 141 (2013), 1759-1773
MSC (2010): Primary 76D55, 35Q30; Secondary 76D05, 93C20
Published electronically: December 7, 2012
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Abstract: We study a Stackelberg strategy subject to the evolutionary Stokes equations, considering a Nash multi-objective equilibrium (not necessarily cooperative) for the ``follower players'' (as they are 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 the Nash equilibrium and its characterization, the approximate controllability of the Stokes system with respect to the leader control and the associate Nash equilibrium, and the existence and uniqueness of the Stackelberg-Nash problem and its characterization.


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Additional Information

F. Guillén-González
Affiliation: Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
Email: guillen@us.es

F. Marques-Lopes
Affiliation: Departamento de Matemática, UFPA, CP 479, 66075-110, Belém-PA, Brazil
Email: fpmlopes@ufpa.br

M. Rojas-Medar
Affiliation: GMA-Departamento de Ciencias Básicas, Universidad del Bío-Bío, Facultad de Ciencias, Campus Fernando May, Casilla 447, Chillán, Chile
Email: marko@ueubiobio.cl

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11459-5
PII: S 0002-9939(2012)11459-5
Keywords: Stokes equations, approximate controllability, multi-objective optimization, Stackelberg-Nash strategies
Received by editor(s): September 14, 2009
Received by editor(s) in revised form: September 15, 2011
Published electronically: December 7, 2012
Additional Notes: The first author was supported in part by the DGI-MEC Grant MTM2006–07932 (Spain), Junta de Andalucía project P06-FQM-02373 (Spain) and Fondecyt-Chile, Grant 1080628.
The third author was supported in part by the DGI-MEC Grant MTM2006–07932 (Spain) and Fondecyt-Chile, Grant 1080628.
Communicated by: Walter Craig
Article copyright: © Copyright 2012 American Mathematical Society