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

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

Abstract

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

CLC Number:

O175.8

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.

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

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