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<p>This research examines the well-posedness and blow-up phenomena associated with a <i>p</i>(<i>l</i>)-biharmonic wave equation characterized by singular dissipation and a variable-exponent logarithmic source term, subject to null Dirichlet boundary conditions. Utilizing contraction mapping principle and Faedo-Galerkin method, the global and local well-posedness of the equation are established. Furthermore, the blow-up behavior, both in finite and infinite time, is demonstrated through the application of a modified concavity argument.</p>

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Well-posedness and blow-up of solutions for the p(l)-biharmonic wave equation with singular dissipation and variable-exponent logarithmic source

  • 期刊论文

  • 发表日期：

    2025年1月28日

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  • Mohammad Shahrouzi,
  • Salah Boulaaras,
  • Rashid Jan

摘要

This research examines the well-posedness and blow-up phenomena associated with a p(l)-biharmonic wave equation characterized by singular dissipation and a variable-exponent logarithmic source term, subject to null Dirichlet boundary conditions. Utilizing contraction mapping principle and Faedo-Galerkin method, the global and local well-posedness of the equation are established. Furthermore, the blow-up behavior, both in finite and infinite time, is demonstrated through the application of a modified concavity argument.