一类强退化方程解的存在惟一性  

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

作　　者：王泽佳[1] 凌征球[2] 柯媛元[1] 

机构地区：[1]吉林大学数学学院 [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

出　　处：《吉林大学学报（理学版）》2007年第2期211-212,共2页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10626024);中国博士后科学基金(批准号:20060390898)

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.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 regularized problem combined with the compensatory solution of the problem considered, then by virtue of the compact theorem, we proved the existence of the weak solution, finally, we showed the uniqueness of the weak solution by using Holmgren＇ s method.

关 键 词：双重退化 正则化问题 Holmgren方法 

分 类 号：O175.8[理学—数学]