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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the approximate controllability of Stackelberg-Nash strategies for Stokes equations
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by F. Guillén-González, F. Marques-Lopes and M. Rojas-Medar PDF
Proc. Amer. Math. Soc. 141 (2013), 1759-1773 Request permission

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
  • MR Author ID: 326792
  • 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
  • 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
  • © Copyright 2012 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1759-1773
  • MSC (2010): Primary 76D55, 35Q30; Secondary 76D05, 93C20
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11459-5
  • MathSciNet review: 3020861