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<p>This paper studies the well–posedness and finite–time blow–up of a strongly damped logarithmic plate equation with a tempered Caputo fractional delay. We prove local well-posedness of weak solutions using semigroup theory and energy estimates. For initial data with negative energy, we show via a refined concavity method that solutions blow up in finite time, highlighting the interplay between the fractional delay, strong damping, and logarithmic nonlinearity. Numerical simulations using a spectral–Newmark scheme confirm the theoretical blow-up behavior.</p>

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Blow-up in a fractionally delayed and strongly damped logarithmic plate equation: theoretical and numerical analysis

  • 期刊论文

  • 发表日期：

    2026年5月2日

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  • Iqra Kanwal,
  • Jianghao Hao,
  • Luqman Bashir,
  • M. Fahim Aslam,
  • Ahmed Bchatnia

摘要

This paper studies the well–posedness and finite–time blow–up of a strongly damped logarithmic plate equation with a tempered Caputo fractional delay. We prove local well-posedness of weak solutions using semigroup theory and energy estimates. For initial data with negative energy, we show via a refined concavity method that solutions blow up in finite time, highlighting the interplay between the fractional delay, strong damping, and logarithmic nonlinearity. Numerical simulations using a spectral–Newmark scheme confirm the theoretical blow-up behavior.