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Dynamics of Kirchhoff Wave Equations Incorporating Energy Damping Effects

  • Pengyan Ding [1] ; Vando Narciso [2]
    1. [1] Henan University of Technology

      Henan University of Technology

      China

    2. [2] State University of Mato Grosso do Sul
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
  • Idioma: inglés
  • Enlaces
  • Resumen

    • In this paper we consider the well-posedness and asymptotic behavior of a Kirchhofftype wave equation under the effects of strong damping whose intensity is given by a non-local degenerate coefficient that depends on the energy associated with the linear part of the system. This class of dissipations is connected with energy damping models proposed by Balakrishnan (A theory of nonlinear damping in flexible structures. Stabilization of flexible structures, 1988) and Balakrishnan-Taylor (Proceedings Damping 89, Flight Dynamics Lab and Air Force Wright Aeronautical Labs, WPAFB, 1989). In our main result, we establish that for each parameter κ associated with the coefficient of the potential part of the Kirchhoff term, the problem has a global attractor Aκ .

      Moreover, we prove that the family of global attractors {Aκ } is upper semi-continuous at κ.

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