具非标准增长条件和正初始能量的非牛顿多方渗流方程

吉林大学学报(理学版)

具非标准增长条件和正初始能量的非牛顿多方渗流方程

刘令¹, 王国铭², 谢嘉宁^3

1. 吉林建筑大学基础科学部, 长春 130118； 2. 吉林大学数学学院, 长春 130012；3. 东北财经大学数学与数量经济学院, 辽宁大连 116025

收稿日期:2013-05-13 出版日期:2013-11-26 发布日期:2013-11-21
通讯作者: 王国铭 E-mail:wanggm@jlu.edu.cn

Blowup of Solution for NonNewtonian Polytropic Filtration EquationInvolving Nonstandard Growth Condition and Positive Initial Energy〖

LIU Ling¹, WANG Guoming², XIE Jianing³

1. Department of Basic Science, Jilin Jianzhu University, Changchun 130118, China;2. College of Mathematics, Jilin University, Changchun 130012, China; 3. School of Mathematics andQuantitative Economics, Dongbei University of Finance and Economics, Dalian 116025, Liaoning Province, China

Received:2013-05-13 Online:2013-11-26 Published:2013-11-21
Contact: WANG Guoming E-mail:wanggm@jlu.edu.cn

摘要/Abstract

摘要：

通过构造合适的控制函数, 利用能量估计法并结合Gronwall不等式的讨论, 研究具变指数源函数的非牛顿多方渗流方程解的爆破性质. 结果表明, 当初始能量为正时, 解在有限时刻爆破.

关键词: 正初始能量, 非标准增长条件, 非牛顿多方渗流方程

Abstract:

The authors studied blowup properties of solutions to a polytropic filtration equation with variable exponent of nonlinearity. By constructing a suitable control function, applying energy estimates method and Gronwall’s inequalities, we proved that the solution of the above problem blows up in finite time when the initial energy is positive.

Key words: positive initial energy, nonstandard growth condition, NonNewtonian polytropic filtration equation

中图分类号:

O175.8

刘令, 王国铭, 谢嘉宁. 具非标准增长条件和正初始能量的非牛顿多方渗流方程[J]. 吉林大学学报(理学版), 2013, 51(06): 1077-1080.

LIU Ling, WANG Guoming, XIE Jianing. Blowup of Solution for NonNewtonian Polytropic Filtration EquationInvolving Nonstandard Growth Condition and Positive Initial Energy〖[J]. Journal of Jilin University Science Edition, 2013, 51(06): 1077-1080.