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<p>This paper investigates a viscoelastic shear beam model under various boundary conditions. We prove the existence and uniqueness of solutions using the Faedo-Galerkin method and establish exponential stability through a Lyapunov functional. A numerical framework is developed using finite element discretization in space and a semi-implicit Euler scheme in time. We demonstrate that the discrete energy decays exponentially and derive a priori error estimates ensuring linear convergence. Numerical simulations are provided to support the theoretical findings.</p>

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Asymptotic behavior of viscoelastic shear beam model: theoretical and numerical studies

  • 期刊论文

  • 发表日期：

    2026年7月29日

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  • My Driss Aouragh,
  • Mustapha El Baz,
  • Toufic El Arwadi,
  • Toni Sayah

摘要

This paper investigates a viscoelastic shear beam model under various boundary conditions. We prove the existence and uniqueness of solutions using the Faedo-Galerkin method and establish exponential stability through a Lyapunov functional. A numerical framework is developed using finite element discretization in space and a semi-implicit Euler scheme in time. We demonstrate that the discrete energy decays exponentially and derive a priori error estimates ensuring linear convergence. Numerical simulations are provided to support the theoretical findings.