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<p>We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function <i>V</i> depending on the space variable in front of the power nonlinearity and an inhomogeneous term <i>W</i> depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2134_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(W\equiv 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo>≡</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2134_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">\(W\not \equiv 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo>≢</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of <i>V</i> and <i>W</i> are discussed in detail.</p>

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Semilinear Wave Inequalities with Double Damping and Potential Terms on Riemannian Manifolds

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Mohamed Jleli,
  • Michael Ruzhansky,
  • Bessem Samet,
  • Berikbol T. Torebek

摘要

We study a semilinear wave inequality with double damping on a complete noncompact Riemannian manifold. The considered problem involves a potential function V depending on the space variable in front of the power nonlinearity and an inhomogeneous term W depending on both time and space variables. Namely, we establish sufficient conditions for the nonexistence of weak solutions in both cases: \(W\equiv 0\) W ≡ 0 and \(W\not \equiv 0\) W ≢ 0 . The obtained conditions depend on the parameters of the problem as well as the geometry of the manifold. Some special cases of manifolds, and of V and W are discussed in detail.