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<p>In this paper, we investigate the blow-up of solutions of a coupled system of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2896_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\((\alpha ,\beta )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-Laplacian type of wave equations, including variable exponents in both damping and source terms. Under suitable assumptions on the variable exponents of nonlinearity, we establish a result of a finite-time blow-up for certain solutions with positive-initial energy and, then, for solutions with negative-initial energy.</p>

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A Blow-Up Result for an \((\alpha {,}\beta )\)-Laplacian Coupled System with Variable-Exponent Damping and Source

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Oulia Bouhoufani,
  • Salim Messaoudi

摘要

In this paper, we investigate the blow-up of solutions of a coupled system of \((\alpha ,\beta )\) ( α , β ) -Laplacian type of wave equations, including variable exponents in both damping and source terms. Under suitable assumptions on the variable exponents of nonlinearity, we establish a result of a finite-time blow-up for certain solutions with positive-initial energy and, then, for solutions with negative-initial energy.