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<p>This paper investigates a viscoelastic plate equation featuring variable-exponent nonlocal energy damping and nonlinear source terms. Employing the Nehari and potential well methods, we establish sufficient conditions for the global existence of solutions. Subsequently, we prove the blow up of solutions under appropriate assumptions on the initial data with positive as well as negative initial energy.</p>

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Existence and blow up of solutions for a viscoelastic plate equation with variable-exponent nonlocal energy damping and nonlinear source terms

  • 期刊论文

  • 发表日期：

    2026年3月26日

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  • Mohammad Shahrouzi,
  • Khalid Hammood Al-Jizani

摘要

This paper investigates a viscoelastic plate equation featuring variable-exponent nonlocal energy damping and nonlinear source terms. Employing the Nehari and potential well methods, we establish sufficient conditions for the global existence of solutions. Subsequently, we prove the blow up of solutions under appropriate assumptions on the initial data with positive as well as negative initial energy.