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<p>We peer over a particular genre of fourth-order pseudo-parabolic equation having a logarithmic nonlinear term with it. This is an initial boundary value problem that arises in thin film theory. We considered backward diffusion in this study. The situations when initial energy is subcritical as well as supercritical are investigated. In order to address the energy, we are adopting the method of concavity by Levine for our study. Finite time blow-up of solutions will be established, and an upper and lower limit for blow-up time is determined here.</p>

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Limits for blow-up time of a nonlinear pseudo-parabolic equation

  • 期刊论文

  • 发表日期：

    2026年1月11日

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  • Sushmitha Jayachandran,
  • Gnanavel Soundararajan

摘要

We peer over a particular genre of fourth-order pseudo-parabolic equation having a logarithmic nonlinear term with it. This is an initial boundary value problem that arises in thin film theory. We considered backward diffusion in this study. The situations when initial energy is subcritical as well as supercritical are investigated. In order to address the energy, we are adopting the method of concavity by Levine for our study. Finite time blow-up of solutions will be established, and an upper and lower limit for blow-up time is determined here.