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<p>A <i>p</i>-Laplacian type wave equation with logarithmic nonlinearity and strong damping is studied.&#xa0;We first analyse the existence of local solutions.&#xa0;Then, by making some appropriate assumptions about the parameters in the equation and the initial values, we prove the existence of global solutions as well as finite and infinite time blow-up solutions at subcritical or critical initial energy. Also, it is proved that the finite and infinite time blow-up solutions exist at arbitrarily high initial energy. Especially, we estimate the blow-up time from both below and above.</p>

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Well-Posedness and Dynamics of Solutions for a p-Laplacian Type Wave Equation with Logarithmic Nonlinearity and Strong Damping

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Hang Ding,
  • Jun Zhou

摘要

A p-Laplacian type wave equation with logarithmic nonlinearity and strong damping is studied. We first analyse the existence of local solutions. Then, by making some appropriate assumptions about the parameters in the equation and the initial values, we prove the existence of global solutions as well as finite and infinite time blow-up solutions at subcritical or critical initial energy. Also, it is proved that the finite and infinite time blow-up solutions exist at arbitrarily high initial energy. Especially, we estimate the blow-up time from both below and above.