一类强退化方程解的存在惟一性

一类强退化方程解的存在惟一性

王泽佳¹，², 凌征球³, 柯媛元¹,⁴

1. 吉林大学数学学院, 长春 130012; 2. 东北师范大学数学与统计学院，长春 130024;3. 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； 4. 中山大学数学与计算科学学院, 广州 510275

收稿日期:2007-02-01 修回日期:1900-01-01 出版日期:2007-03-26 发布日期:2007-03-26
通讯作者: 柯媛元

Existence and Uniqueness of Solutions to a Class ofStrongly Degenerate Equations

WANG Zejia¹,², LING Zhengqiu³, KE Yuanyuan¹,⁴

1. College of Mathematics, Jilin University, Changchun 130012, China; 2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024; 3. Department of Mathematics and Computer Science, Yulin Normal University, Yulin 537000, Guangxi Zhuang Autonomous Region, China; 4. School of Mathematics and Computational Science, Sun YatSen University, Guangzhou 510275, China

Received:2007-02-01 Revised:1900-01-01 Online:2007-03-26 Published:2007-03-26
Contact: KE Yuanyuan

摘要/Abstract

摘要： 研究一类含源的具双重强退化方程初边值问题解的存在惟一性, 由于退化的存在使得问题不存在古典解. 通过定义弱解，借助于正则化问题结合紧致补偿定理证明了弱解的存在性, 并在一定条件下利用Holmgren方法证明了弱解的惟一性。

关键词: 双重退化, 正则化问题, Holmgren方法

Abstract: This paper deals with the existence and uniqueness of solutions to a class of doubly strongly degenerate equations. Owing to the degeneracies in the equation, the classical solutions of the problem may not exist. We firstly gave the definition of the weak solution of the problem considered, then by virtue of the regularized problem combined with the compensatory compact theorem, we proved the existence of the weak solution, finally, we showed the uniqueness of the weak solution by using Holmgren’s method.

Key words: doubly strongly degenerate, regularized problem, Holmg ren’s method

中图分类号:

O175.8

王泽佳，, 凌征球, 柯媛元,. 一类强退化方程解的存在惟一性[J]. J4, 2007, 45(02): 211-212.

WANG Zejia,, LING Zhengqiu, KE Yuanyuan,. Existence and Uniqueness of Solutions to a Class ofStrongly Degenerate Equations[J]. J4, 2007, 45(02): 211-212.

[1]	凌征球,, 王泽佳,. 一类双重退化抛物型方程的Cauchy问题[J]. J4, 2006, 44(05): 679-686.
[2]	王泽佳, 李颖花, 王春朋. 双重退化抛物型方程的重整化解[J]. J4, 2005, 43(03): 297-298.