Scholarlink

<p>This paper investigates the well-posedness and asymptotic stability of a semilinear wave equation with variable coefficients, subject to a memory source term and nonlinear boundary feedback. Employing the Faedo-Galerkin method and a denseness argument, we establish the existence and uniqueness of strong and weak solutions. Furthermore, by introducing an equivalent energy functional within a Riemannian geometry framework, we derive the general energy decay rates of the system. Our analysis reveals that the decay rates are primarily influenced by mechanical damping and the memory kernel function. Notably, the stabilization process involves a delicate interplay among the nonlinear term, mechanical damping, memory effects, and the geometric properties of the domain.</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

On a Semilinear Wave Equation in Riemannian Geometric Setting with Memory Source Under the Nonlinear Boundary Feedback

  • 期刊论文

  • 发表日期：

    2025年4月22日

查看全文
  • Sheng-Jie Li,
  • Shugen Chai

摘要

This paper investigates the well-posedness and asymptotic stability of a semilinear wave equation with variable coefficients, subject to a memory source term and nonlinear boundary feedback. Employing the Faedo-Galerkin method and a denseness argument, we establish the existence and uniqueness of strong and weak solutions. Furthermore, by introducing an equivalent energy functional within a Riemannian geometry framework, we derive the general energy decay rates of the system. Our analysis reveals that the decay rates are primarily influenced by mechanical damping and the memory kernel function. Notably, the stabilization process involves a delicate interplay among the nonlinear term, mechanical damping, memory effects, and the geometric properties of the domain.