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<p>This work is concerned with a nonlinear viscoelastic wave equation with logarithmic nonlinearity. By supposing the nonlinear time-varying delay acting on the boundary feedback coupling by the acoustic and fractional boundary conditions. Firstly, we prove the exponential growth of solutions with negative initial-energy under suitable hypotheses and, in general, of the kernel. Then, the blow-up of solutions is showed under the same assumptions. This result extends and complements some previous results.</p>

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Growth and blow-up of solutions for a viscoelastic wave equation with logarithmic source, fractional conditions, and non-linear boundary feedback

  • 期刊论文

  • 发表日期：

    2025年3月18日

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  • Abdelbaki Choucha,
  • Salah Boulaaras,
  • Mohamed Haiour,
  • Mohammad Shahrouzi,
  • Rashid Jan,
  • Mohamed Abdalla

摘要

This work is concerned with a nonlinear viscoelastic wave equation with logarithmic nonlinearity. By supposing the nonlinear time-varying delay acting on the boundary feedback coupling by the acoustic and fractional boundary conditions. Firstly, we prove the exponential growth of solutions with negative initial-energy under suitable hypotheses and, in general, of the kernel. Then, the blow-up of solutions is showed under the same assumptions. This result extends and complements some previous results.