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<p>The purpose of this work is to investigate the stabilization of a locally coupled wave-Euler Bernoulli beam equations with local Kelvin–Voigt dampings. In this paper, we study three cases: The case when the supports of the dampings and the coupling coefficients are disjoint and in the second and the third cases, we assume that there is an intersection between the damping and coupling regions. First, using a general criteria of Arendt–Batty (Tauberian theorems and stability of one-parameter semigroups. Trans Am Math Soc 306(2):837–852, 1988), combined with an uniqueness result, we prove that our system is strongly stable. Next, using a frequency domain approach, combined with a piecewise multiplier technique we show the polynomial stability.</p>

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Stability results of locally coupled wave and Euler Bernoulli equations with local Kelvin–Voigt dampings

  • 期刊论文

  • 发表日期：

    2025年3月26日

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  • Wafa Ahmedi,
  • Akram Ben Aissa

摘要

The purpose of this work is to investigate the stabilization of a locally coupled wave-Euler Bernoulli beam equations with local Kelvin–Voigt dampings. In this paper, we study three cases: The case when the supports of the dampings and the coupling coefficients are disjoint and in the second and the third cases, we assume that there is an intersection between the damping and coupling regions. First, using a general criteria of Arendt–Batty (Tauberian theorems and stability of one-parameter semigroups. Trans Am Math Soc 306(2):837–852, 1988), combined with an uniqueness result, we prove that our system is strongly stable. Next, using a frequency domain approach, combined with a piecewise multiplier technique we show the polynomial stability.