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Exponential stabilization of a structural acoustic model arising in the control of noise

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Abstract

We consider a coupled hybrid system whose main application is the problem of the active control of noise. The model describes the interaction of acoustic vibrations in the interior of a given two-dimensional cavity with the mechanical vibrations of two damped strings located in a part of the boundary of the cavity, in which suitable feedbacks are acting. Our main result is that the total energy associated to this model decays exponentially as time goes to infinity.

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Acknowledgements

Octavio Vera is partially financed by Project Fondecyt 1191137 and UTA MAYOR 2022–2023, 4764-22. R. Díaz was supported by project GIAP14/21, Grupo de investigación en análisis y modelamiento matemático, Universidad de los Lagos, Osorno. R.Díaz and N. Zumelzu was supported by the University of Magallanes (UMAG) under Project 021016 and the National Research and Development Agency of Chile (ANID Chile) through the FONDEF IDEA I+D project ID23I10288.

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Authors and Affiliations

  1. Departamento de Ciencias Exactas, Universidad de Los Lagos, Osorno, Chile

    Roberto Díaz

  2. Instituto Militar de Engenharia – IME, Rio de Janeiro, Brazil

    Marcio V. Ferreira

  3. Departamento de Matemática, Universidad del Bío-Bío, Concepcion, Chile

    Jaime Muñoz

  4. Departamento de Matemática, Universidad de Tarapacá, Arica, Chile

    Octavio Vera

  5. Departamento de Matemática y Física, Universidad de Magallanes, Punta Arenas, Chile

    Nicolás Zumelzu

Authors
  1. Roberto Díaz
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  2. Marcio V. Ferreira
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  3. Jaime Muñoz
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  4. Octavio Vera
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  5. Nicolás Zumelzu
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Correspondence to Roberto Díaz.

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Díaz, R., Ferreira, M.V., Muñoz, J. et al. Exponential stabilization of a structural acoustic model arising in the control of noise. Comp. Appl. Math. 43, 202 (2024). https://doi.org/10.1007/s40314-024-02734-2

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  • DOI: https://doi.org/10.1007/s40314-024-02734-2

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