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<p>This paper studies the global existence of large perturbation solutions for the thin film growth model, a class of fourth-order nonlinear parabolic equations. The main purpose of this paper is to attempt to find an effective method to capture the enhanced dissipation mechanism generated by the fourth-order parabolic equation and the Couette flow in the full-space case through the Green’s function, thereby suppressing the blow-up of the solutions for the nonlinear parabolic equation and obtaining the overall existence of the solutions.</p>

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The Green’s Function Method and Thin Film Growth Model with Couette Flow

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Jie Qi,
  • Weike Wang

摘要

This paper studies the global existence of large perturbation solutions for the thin film growth model, a class of fourth-order nonlinear parabolic equations. The main purpose of this paper is to attempt to find an effective method to capture the enhanced dissipation mechanism generated by the fourth-order parabolic equation and the Couette flow in the full-space case through the Green’s function, thereby suppressing the blow-up of the solutions for the nonlinear parabolic equation and obtaining the overall existence of the solutions.