In this paper, we show the existence and uniqueness of time-periodic solutions for the viscous Cahn–Hilliard equation with the homogeneous Dirichlet boundary condition. We also investigate the asymptotic limit of time-periodic solutions of the viscous Cahn–Hilliard equation to time-periodic solutions of the Allen–Cahn equation or the Cahn–Hilliard equation. We here assume that the nonlinear term can be decomposed into the difference between a maximal monotone part and its perturbation, by which we can exclude the Sobolev subcritical growth condition on the nonlinear term which is frequently assumed in previous studies.

中文翻译：

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具有齐次 Dirichlet 边界条件的粘性 Cahn-Hilliard 方程的时间周期问题

在本文中，我们证明了具有齐次 Dirichlet 边界条件的粘性 Cahn-Hilliard 方程的时间周期解的存在性和唯一性。我们还研究了粘性 Cahn-Hilliard 方程的时间周期解对 Allen-Cahn 方程或 Cahn-Hilliard 方程的时间周期解的渐近极限。我们在这里假设非线性项可以分解为最大单调部分与其扰动之间的差异，由此我们可以排除以前研究中经常假设的非线性项的 Sobolev 亚临界增长条件。