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<p>In this paper, we study the initial boundary value problem for the equation modeling thin-film growth with logarithmic nonlinearity. Using the potential well method, we obtain the blow-up phenomena of weak solutions for subcritical initial energy and critical initial energy.Furthermore, we estimate an upper bound and a lower bound for the blow-up time. When the initial energy is independent of the well depth, we provide a sufficient condition for the solution to blow up in finite time and derive an upper bound for the blow-up time.</p>

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Blow-up results for a fourth-order parabolic equation modeling thin-film growth with logarithmic nonlinearity

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Wei Zhang,
  • Jialing Zhang

摘要

In this paper, we study the initial boundary value problem for the equation modeling thin-film growth with logarithmic nonlinearity. Using the potential well method, we obtain the blow-up phenomena of weak solutions for subcritical initial energy and critical initial energy.Furthermore, we estimate an upper bound and a lower bound for the blow-up time. When the initial energy is independent of the well depth, we provide a sufficient condition for the solution to blow up in finite time and derive an upper bound for the blow-up time.