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On a multi-objective control problem for the Korteweg–de Vries equation

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Abstract

This paper deals with a hierarchical control problem for the Korteweg–de Vries (KdV) equation with distributed controls following a Stackelberg–Nash strategy. We have a control problem with many objectives to be achieved and, to do that, more than one control is needed. We assume that there is a primary control, called the leader, and two secondary ones, called the followers, each of them responsible for a given objective. Once the leader has fixed its goals, the followers must act to accomplish their ones. In the present paper, the leader wants to drive the solutions of a KdV equation to a given trajectory, while the followers must be in equilibrium according to their targets. We stress that results of this kind are already known for many parabolic and hyperbolic equations, but no results are known for any dispersive equation.

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Acknowledgements

The research was partially supported by Grant 2019/0014 Paraíba State Research Foundation (FAPESQ), CNPq, CAPES, MathAmSud ACIPDE and SCIPinPDEs.

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Authors and Affiliations

  1. Universidade de Pernambuco, Nazaré da Mata, PE, 55800-000, Brazil

    Islanita C. A. Albuquerque

  2. Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa, PB, 58051-900, Brazil

    Fágner D. Araruna & Maurício C. Santos

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  1. Islanita C. A. Albuquerque
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  2. Fágner D. Araruna
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  3. Maurício C. Santos
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Correspondence to Maurício C. Santos.

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Communicated by Enno Lenzmann.

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Albuquerque, I.C.A., Araruna, F.D. & Santos, M.C. On a multi-objective control problem for the Korteweg–de Vries equation. Calc. Var. 62, 131 (2023). https://doi.org/10.1007/s00526-023-02471-0

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