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<p>This paper considers a class of fourth-order singular parabolic equations with a viscoelastic term. We utilize the cut-off technique to deal with the singular potential and establish the local solvability by combining with the Galerkin method and the contraction mapping principle. Furthermore, based on the framework of modified potential well, we use Hardy–Sobolev inequality to get the global existence and a general decay rate estimate. Lastly, the finite time blow-up of weak solutions is proved and the upper bound for blow-up time under certain conditions is obtained.</p>

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Asymptotic Behavior and Blow-Up of Solutions for a Singular Parabolic Equation with Viscoelastic Term

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Xiulan Wu,
  • Yaxin Zhao

摘要

This paper considers a class of fourth-order singular parabolic equations with a viscoelastic term. We utilize the cut-off technique to deal with the singular potential and establish the local solvability by combining with the Galerkin method and the contraction mapping principle. Furthermore, based on the framework of modified potential well, we use Hardy–Sobolev inequality to get the global existence and a general decay rate estimate. Lastly, the finite time blow-up of weak solutions is proved and the upper bound for blow-up time under certain conditions is obtained.