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<p>A fourth-order <i>p</i>-Laplacian equation with a second-order <i>q</i>-Laplacian diffusion and a nonlinear source function is studied by using potential well theory. For this purpose, we introduce two necessary functionals with respect to weak solutions, which divide the initial conditions into three cases: subcritical, critical and supcritical cases. The existence, blow up behavior and long time decay of solutions are analyzed according to those initial energy cases with different conditions for parameters.</p>

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On a p-Laplacian equation with a second-order q-Laplacian diffusion of fourth-order

  • 期刊论文

  • 发表日期：

    2025年3月12日

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  • Bo Liang,
  • Sitong Liu,
  • Yongfeng Ma

摘要

A fourth-order p-Laplacian equation with a second-order q-Laplacian diffusion and a nonlinear source function is studied by using potential well theory. For this purpose, we introduce two necessary functionals with respect to weak solutions, which divide the initial conditions into three cases: subcritical, critical and supcritical cases. The existence, blow up behavior and long time decay of solutions are analyzed according to those initial energy cases with different conditions for parameters.