Cahn-Hilliard和粘性Cahn-Hilliard方程解的最大值估计
The Maximum Estimate of Solution to the Cahn-Hilliard Equation and Viscous Cahn-Hilliard Equation
摘要: 本文研究了具有一般非线性条件的Cahn-Hilliard方程和粘性Cahn-Hilliard方程解的最大值估 计。首先，我们用能量估计的方法得到解的Lq 范数有界。然后，利用Nirenberg-Gagliado不等式得到解的本性上确界有界。
Abstract: In this paper, our aim is to prove the maximum estimates of solutions to the Cahn- Hilliard equation and Viscous Cahn-Hilliard equation with a general nonlinear source term. Firstly, we obtain the boundedness of the Lq norm by using energy estimates. Then, the boundedness of essential supremum is demonstrated by Nirenberg-Gagliado inequality.
文章引用：薛春香, 蒲志林. Cahn-Hilliard和粘性Cahn-Hilliard方程解的最大值估计[J]. 应用数学进展, 2022, 11(1): 526-536. https://doi.org/10.12677/AAM.2022.111060

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