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<p>The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2934_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\( p \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> </InlineEquation>-Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.</p>

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Asymptotic Analysis of Solutions for a p-Kirchhoff Type Hyperbolic Equation with Dynamic Boundary Conditions

  • 期刊论文

  • 发表日期：

    2025年8月17日

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  • Billel Gheraibia,
  • Nouri Boumaza,
  • Adel M. Al-Mahdi,
  • Mohammad M. Al-Gharabli

摘要

The aim of this study is to analyze the global existence, general decay, and blow-up behavior of solutions for a class of \( p \) p -Kirchhoff-type hyperbolic equations with damping terms and dynamic boundary conditions. The global existence of solutions is demonstrated using potential well theory, while the general decay of energy—encompassing exponential and polynomial decay as particular cases—is established through multiplier techniques combined with nonlinear integral inequalities. Finally, the blow-up of solutions is proven in the case of negative initial energy.