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<p>In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.</p>

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Well-Posedness and Asymptotic Analysis of Wave Equation with Nonlocal Boundary Damping

  • 期刊论文

  • 发表日期：

    2025年9月30日

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  • Marcelo M. Cavalcanti,
  • Adel M. Al-Mahdi,
  • Mohammad M. Al-Gharabli,
  • Cintya A. Okawa

摘要

In this work, we study a wave equation with nonlocal boundary damping of energy type. We begin by establishing the well-posedness of the problem using the Galerkin method. Next, we investigate the asymptotic behavior of the solution by applying the multiplier method, and we enhance the decay rate through the use of Nakao’s Lemma. Finally, we employ the radial multiplier technique to obtain an optimal polynomial decay rate under this type of damping.