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<p>Using variational methods, Zhao (Acta Mathematica Scientia 31A(6):1461–1469, 2011) established nonlinear governing equations and nonlinear boundary conditions on the peeling front for peeling thin films from substrates by pulling one side upwards. For constant pulling speed, the model admits constant peeling speed. In the paper, employing the method of characteristics, we demonstrate the stability of such a constant background solution. That is, the model still admits a classical solution when the perturbation on the pulling speed is small and its derivative is with algebraic decay. Additionally, we also prove that if the perturbation on the pulling speed decays to zero, the speed of the peeling fronts also decays to the constant peeling speed of the background solutions.</p>

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On the Global Classical Solution of Peeling Models

  • 期刊论文

  • 发表日期：

    2025年2月25日

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  • Qianfeng Li,
  • Yongqian Zhang

摘要

Using variational methods, Zhao (Acta Mathematica Scientia 31A(6):1461–1469, 2011) established nonlinear governing equations and nonlinear boundary conditions on the peeling front for peeling thin films from substrates by pulling one side upwards. For constant pulling speed, the model admits constant peeling speed. In the paper, employing the method of characteristics, we demonstrate the stability of such a constant background solution. That is, the model still admits a classical solution when the perturbation on the pulling speed is small and its derivative is with algebraic decay. Additionally, we also prove that if the perturbation on the pulling speed decays to zero, the speed of the peeling fronts also decays to the constant peeling speed of the background solutions.