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Bi-objective and hierarchical control for the Burgers equation

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Abstract

We present some results concerning the control of the Burgers equation. We analyze a bi-objective optimal control problem and then the hierarchical null controllability through a Stackelberg–Nash strategy, with one leader and two followers. The results may be viewed as an extension to this nonlinear setting of a previous analysis performed for linear and semilinear heat equations. They can also be regarded as a first step in the solution of control problems of this kind for the Navier–Stokes equations.

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Authors and Affiliations

  1. Dpto. de Matemática, Universidade Federal da Paraíba, João Pessoa, PB,  58051-900, Brazil

    F. D. Araruna

  2. Dpto. EDAN and IMUS, University of Sevilla, Aptdo. 1160, 41080, Sevilla, Spain

    E. Fernández-Cara

  3. Dpto. de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, 58051-900, Brazil

    E. Fernández-Cara

  4. Instituto Federal do Rio Grande do Norte, João Câmara, RN, 59550-000, Brazil

    L. C. da Silva

Authors
  1. F. D. Araruna
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  2. E. Fernández-Cara
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  3. L. C. da Silva
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Correspondence to F. D. Araruna.

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F. D. Araruna: Partially supported by Grant 2019/0014 Paraíba State Research Foundation (FAPESQ), CNPq, CAPES (Brazil) and MathAmSud SCIPinPDEs. E. Fernández-Cara: Partially supported by DGI-MINECO (Spain, Grant PID2020-114976GB-I00). L. C. da Silva: Partially supported by CAPES (Brazil).

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Araruna, F.D., Fernández-Cara, E. & da Silva, L.C. Bi-objective and hierarchical control for the Burgers equation. J. Evol. Equ. 24, 30 (2024). https://doi.org/10.1007/s00028-024-00952-z

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