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<p>In this paper, we study the wave equation with a distributed delay and a logarithmic source terms. By combined the Fractional condition with distributed delay term, we prove the existence and uniqueness of the solutions using the semi-group theory and the energy method. We then study the global existence of solutions with suitable conditions that we used in the next section on general decay of solutions, by constructing a suitable and carefully selected Lyapunov function. We believe we are the first to address this type of problem, especially the application of the fractional condition to distributed delay.</p>

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Well posedness and general decay for a wave equation with logarithmic source term and distributed delay of fractional type

  • 期刊论文

  • 发表日期：

    2025年6月19日

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  • Abdelbaki Choucha,
  • Salah Boulaaras,
  • Behzad Djafari Rouhani

摘要

In this paper, we study the wave equation with a distributed delay and a logarithmic source terms. By combined the Fractional condition with distributed delay term, we prove the existence and uniqueness of the solutions using the semi-group theory and the energy method. We then study the global existence of solutions with suitable conditions that we used in the next section on general decay of solutions, by constructing a suitable and carefully selected Lyapunov function. We believe we are the first to address this type of problem, especially the application of the fractional condition to distributed delay.