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<p>In this paper, the initial boundary value problem of the wave equation with source term and logarithmic damping term is considered. The global existence of solutions is proved by means of semigroup theory combined with the stable set method. By Nakao’s inequality combined with some special algebra inequalities for logarithmic function, the exponential stability of solutions is obtained for two classes of logarithmic damping terms. These results improve upon those in the previous literature.</p>

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Semigroup Well-posedness and Exponential Stability for the Wave Equation With Source and Logarithmic Damping Terms

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Donghao Li,
  • Hongwei Zhang

摘要

In this paper, the initial boundary value problem of the wave equation with source term and logarithmic damping term is considered. The global existence of solutions is proved by means of semigroup theory combined with the stable set method. By Nakao’s inequality combined with some special algebra inequalities for logarithmic function, the exponential stability of solutions is obtained for two classes of logarithmic damping terms. These results improve upon those in the previous literature.