Weak solutions for the functionalized Cahn–Hilliard equation with degenerate mobility
Weak solutions for the functionalized Cahn–Hilliard equation with degenerate mobility
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DOI：
10.1080/00036811.2019.1585536
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发表时间：
2019-03
影响因子：
1.1
通讯作者：
Shibin Dai;Qiang Liu;K. Promislow
中科院分区：
文献类型：
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作者：
Shibin Dai;Qiang Liu;K. Promislow
功能化的卡恩-希利亚德自由能描述了溶剂中两亲分子混合物的相分离。应用于高度两亲性分子（例如脂质）需要简并扩散，消除体扩散，从而产生表面驱动扩散。我们研究了包含简并迁移率的函数化 Cahn-Hilliard 方程的梯度流弱解的存在性，捕获解作为具有非简并迁移率的方程弱解的极限。
The functionalized Cahn–Hilliard free energy describes phase separation in mixtures of amphiphilic molecules in solvent. Applications to highly amphiphilic molecules such as lipids requires degenerate diffusion that eliminates bulk diffusion, resulting in surface driven diffusion. We study the existence of weak solutions of a gradient flow of the functionalized Cahn–Hilliard equation that incorporates degenerate mobility, capturing solutions as limits of the weak solution for equations with non-degenerate mobilities.