On nonnegative solutions for the Functionalized Cahn-Hilliard equation with degenerate mobility

被引：7

作者：

Dai, Shibin ^{[1
]}

Liu, Qiang ^{[2
]}

Luong, Toai ^{[1
]}

Promislow, Keith ^{[3
]}

机构：

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Shenzhen Univ, Coll Math & Stat, Shenzhen 518060, Peoples R China

[3] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

RESULTS IN APPLIED MATHEMATICS | 2021年 / 12卷

基金：

美国国家科学基金会;

关键词：

Weak solutions; Nonnegative solutions; The Functionalized Cahn-Hilliard equation; Degenerate mobility; ELASTIC BENDING ENERGY; INTERFACES;

D O I：

10.1016/j.rinam.2021.100195

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Functionalized Cahn-Hilliard equation has been proposed as a model for the interfacial energy of phase-separated mixtures of amphiphilic molecules. We study the existence of a nonnegative weak solutions of a gradient flow of the Functionalized Cahn-Hilliard equation subject to a degenerate mobility M(u) that is zero for u <= 0. Assuming the initial data u(0)(x) is positive, we construct a weak solution as the limit of solutions corresponding to non-degenerate mobilities and verify that it satisfies an energy dissipation inequality. Our approach is a combination of Galerkin approximation, energy estimates, and weak convergence methods. (C) 2021 The Author(s). Published by Elsevier B.V.

引用

页数：13

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