一类带梯度依赖势和源的粘性Cahn-Hilliard方程的爆破现象

数学物理学报 ›› 2019, Vol. 39 ›› Issue (3): 510-517.

一类带梯度依赖势和源的粘性Cahn-Hilliard方程的爆破现象

龙群飞^1,*(),陈建清²

¹ 贵州师范大学数学科学学院贵阳 550025
² 福建师范大学数学与信息学院/数学研究中心福州 350177

收稿日期:2017-11-10 出版日期:2019-06-26 发布日期:2019-06-27
通讯作者: 龙群飞 E-mail:qflongfjnu@126.com
基金资助:
国家自然科学基金（青年项目）(11401100);国家自然科学基金(11371091);国家自然科学基金(11161057);非线性分析及其应用创新团队(IRTL1206)

Blow-Up Phenomena of Solutions for a Class of Viscous Cahn-Hilliard Equation with Gradient Dependent Potentials and Sources

Qunfei Long^1,*(),Jianqing Chen²

¹ School of Mathematical Sciences, Guizhou Normal University, Guiyang 550025
² Department of Mathematics & FJKLMAA, Fujian Normal University, Fuzhou 350117

Received:2017-11-10 Online:2019-06-26 Published:2019-06-27
Contact: Qunfei Long E-mail:qflongfjnu@126.com
Supported by:
the NSFC (Youth Fund)(11401100);the NSFC(11371091);the NSFC(11161057);the Innovation Group of 'Nonlinear Analysis and Its Applications'(IRTL1206)

摘要/Abstract

摘要：

该文讨论了一类带梯度依赖势和源的粘性Cahn-Hilliard方程解的爆破现象.使用能量方法，微分不等式和积的导数公式建立了爆破准则和确定了爆破时间的上界；利用微分不等式和积的导数公式确定了爆破时间的下界.

关键词: 粘性Cahn-Hilliard方程, 爆破时间的界, 爆破准则, 微分不等式, 积的导数公式

Abstract:

In this manuscript, we study the blow-up phenomena of solutions for a class of viscous Cahn-Hilliard equation with gradient dependent potentials and source. We establish a criterion for blow-up and determine the upper bound for blow-up time by the energy method, the differential inequality and the derivative formula of the product; We determine the lower bounds for blow-up time by the differential inequality and the derivative formula of the product.

Key words: Viscous Cahn-Hilliard equation, Bounds for blow-up time, Criteria for the low-up, Differential inequality, Derivative formula of the product

中图分类号:

O175

龙群飞,陈建清. 一类带梯度依赖势和源的粘性Cahn-Hilliard方程的爆破现象[J]. 数学物理学报, 2019, 39(3): 510-517.

Qunfei Long,Jianqing Chen. Blow-Up Phenomena of Solutions for a Class of Viscous Cahn-Hilliard Equation with Gradient Dependent Potentials and Sources[J]. Acta mathematica scientia,Series A, 2019, 39(3): 510-517.

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