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<p>In this paper, we investigate a nonlinear coupled fourth-order parabolic problem. We surmount the difficulty stemming from the nonlinear coupled relationship between the two components of weak solutions when defining appropriate auxiliary functions, energy functionals, and corresponding manifold. Subsequently, we establish an optimal classification of initial energy, for which blow-up and global solutions are respectively derived. For all cases under consideration, we deduce large-time estimates for global solutions. Furthermore, for subcritical and supercritical initial energy scenarios, we obtain explicit bounds on the blow-up time and blow-up rates.</p>

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Blow-up rate and time in a nonlinear coupled fourth-order parabolic problem

  • 期刊论文

  • 发表日期：

    2025年7月25日

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  • Bingchen Liu,
  • Yang Li

摘要

In this paper, we investigate a nonlinear coupled fourth-order parabolic problem. We surmount the difficulty stemming from the nonlinear coupled relationship between the two components of weak solutions when defining appropriate auxiliary functions, energy functionals, and corresponding manifold. Subsequently, we establish an optimal classification of initial energy, for which blow-up and global solutions are respectively derived. For all cases under consideration, we deduce large-time estimates for global solutions. Furthermore, for subcritical and supercritical initial energy scenarios, we obtain explicit bounds on the blow-up time and blow-up rates.