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<p>An initial boundary value problem for a class of nonlinear wave equations with localized internal damping and a nonlinear acoustic boundary conditions of Kirchhoff type is considered. Existence, uniqueness, and stability of solutions are established. To prove the existence of solution, we use Faedo–Galerkin method, and due to the presence of nonconstant coefficients in the boundary equation, new estimates are necessary. To prove the stability, we use multiplier method.</p>

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On a class of wave equations with a nonlinear dynamic boundary condition of Kirchhoff type

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月27日

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  • Cícero Lopes Frota,
  • André Vicente

摘要

An initial boundary value problem for a class of nonlinear wave equations with localized internal damping and a nonlinear acoustic boundary conditions of Kirchhoff type is considered. Existence, uniqueness, and stability of solutions are established. To prove the existence of solution, we use Faedo–Galerkin method, and due to the presence of nonconstant coefficients in the boundary equation, new estimates are necessary. To prove the stability, we use multiplier method.