Scholarlink

<p>The long-time behaviour of solutions to a wave viscoelastic equation with nonlocal boundary dissipation and memory is considered in this work. The existence of a regular global solution of the considered problem is proved through the Galerkin method combined with Aubin-Lions compactness arguments. Then, using the multiplier method, we construct explicit formulas depending on some conditions, which prove that the energy of the considered model decays towards zero in an exponential or polynomial manner. Moreover, we prove that the studied problem has an absorbing set for a particular case. The existence of global attractor with finite fractal dimensions is obtained by the useful properties of asymptotic smoothness and quasi-stability. This will enables us to deduce sufficient conditions on the existence of exponential and global minimal attractors.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Limit Behavior of a Viscoelastic Equation with Mixed Dirichlet and Neumann Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年12月12日

查看全文
  • Moncef Aouadi,
  • Lin-fang Liu

摘要

The long-time behaviour of solutions to a wave viscoelastic equation with nonlocal boundary dissipation and memory is considered in this work. The existence of a regular global solution of the considered problem is proved through the Galerkin method combined with Aubin-Lions compactness arguments. Then, using the multiplier method, we construct explicit formulas depending on some conditions, which prove that the energy of the considered model decays towards zero in an exponential or polynomial manner. Moreover, we prove that the studied problem has an absorbing set for a particular case. The existence of global attractor with finite fractal dimensions is obtained by the useful properties of asymptotic smoothness and quasi-stability. This will enables us to deduce sufficient conditions on the existence of exponential and global minimal attractors.