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<p>In this work, we investigate the logarithmic nonlinear wave equation, which is distinguished by strong time-varying delay components, infinite memory, and strong damping. Through semigroup theory, we have established a local existence result, paving the way for a comprehensive understanding of the equation’s behavior. In addition, we explore the global existence of solutions, revealing fascinating decay results and investigating the circumstances in which blow-up may occur in solutions with negative starting energy. Our results shed light on the complex nature of this dynamic system while also strengthening the theoretical framework.</p>

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Exponential decay and blow-up results of a logarithmic nonlinear wave equation having infinite memory and strong time-varying delay

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月6日

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  • Luqman Bashir,
  • Jianghao Hao,
  • Salah Boulaaras,
  • Muhammad Fahim Aslam,
  • Tong Zhang

摘要

In this work, we investigate the logarithmic nonlinear wave equation, which is distinguished by strong time-varying delay components, infinite memory, and strong damping. Through semigroup theory, we have established a local existence result, paving the way for a comprehensive understanding of the equation’s behavior. In addition, we explore the global existence of solutions, revealing fascinating decay results and investigating the circumstances in which blow-up may occur in solutions with negative starting energy. Our results shed light on the complex nature of this dynamic system while also strengthening the theoretical framework.