一类Cahn-Hilliard方程弱解的存在惟一性

一类Cahn-Hilliard方程弱解的存在惟一性

柴世民, 尹云光, 宫成春, 尹丽

吉林大学数学学院, 长春 130012

收稿日期:2007-11-20 修回日期:1900-01-01 出版日期:2008-05-26 发布日期:2008-05-26
通讯作者: 宫成春

Existence and Uniqueness of Weak Solutions fora Class of CahnHilliard Equations

CHAI Shimin, YIN Yunguang, GONG Chengchun, YIN Li

College of Mathematics, Jilin University, Changchun 130012, China

Received:2007-11-20 Revised:1900-01-01 Online:2008-05-26 Published:2008-05-26
Contact: GONG Chengchun

摘要/Abstract

摘要： 讨论一类具有非定常系数迁移率的CahnHilliard方程. 针对迁移率为m(x,t)的情形, 通过引入Nirenberg不等式给出了解的有界性先验估计,并应用LeraySchauder不动点定理证明了此类Cahn-Hilliard方程弱解的存在惟一性.

关键词: Cahn-Hilliard方程, Nirenberg不等式, LeraySchauder不动点定理

Abstract: A class of the CahnHilliard equations with nonconstant mobility was studied. With the aid of Nirenberg’sinequality, some priori estimates are presented in the case of the mobility is m(x,t). Then the existence and uniqueness of the weak solutions are given by means of LeraySchauder fixed point theorem.

Key words: CahnHilliard equation, Nirenberg inequality, Leray Schauder fixed point theorem

中图分类号:

O175.29

柴世民, 尹云光, 宫成春, 尹丽. 一类Cahn-Hilliard方程弱解的存在惟一性[J]. J4, 2008, 46(03): 453-456.

CHAI Shimin, YIN Yunguang, GONG Chengchun, YIN Li. Existence and Uniqueness of Weak Solutions fora Class of CahnHilliard Equations[J]. J4, 2008, 46(03): 453-456.

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