| 一类双重退化抛物型方程的Cauchy问题 |
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| 引用本文： | 凌征球,王泽佳.一类双重退化抛物型方程的Cauchy问题[J].吉林大学学报(理学版),2006,44(5):679-686. |
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| 作者姓名： | 凌征球 王泽佳 |
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| 作者单位： | 1. 吉林大学 数学研究所, 长春 130012; 2. 玉林师范学院 数学与计算机科学系, 广西壮族自治区 玉林 537000; 3. 东北师范大学 数学与统计学院, 长春 130024; 4. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 研究一类双重退化抛物型方程的Cauchy问题, 给出了弱解 熵解的定义, 并借助于正则化问题利用补偿紧致定理证明了问题熵解的存在性, 利用双变量方法得到这种弱解的稳定性.
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| 关 键 词： | 双重退化抛物方程 熵解 稳定性 |
| 文章编号： | 1671-5489(2006)05-0679-08 |
| 收稿时间： | 2005-12-30 |
| 修稿时间： | 2005年12月30 |
Cauchy Problems for a Class of Doublely Degenerate Parabolic Equations |
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| LING Zheng-qiu,WANG Ze-jia.Cauchy Problems for a Class of Doublely Degenerate Parabolic Equations[J].Journal of Jilin University: Sci Ed,2006,44(5):679-686. |
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| Authors: | LING Zheng-qiu WANG Ze-jia |
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| Institution: | 1. Institute of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Mathematics and Computer Science, Yulin Normal University, Yulin 537000, Guangxi Zhuang Autonomous Region, China;3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;4. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | This paper is concerned with the Cauchy problem for a class of degenerate parabolic equations,which describes the movement of liquid in porous media,i.e.,filtration.The definitions of the entropy solution and the weak solution were proposed,then by virtue of the regularized problem,the existence of the entropy solution was shown by using the compensatory compact theorem.Furthermore,the stability of the entropy solution was obtained by the double variable method. |
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| Keywords: | doublely degenerate parabolic equation entropy solution stability |
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