带抛物退化线的二阶混合型方程的间断斜微商(英文)  

Discontinuous Oblique Derivative Problems for Second Order Mixed Equations with Parabolic Degeneracy

作　　者：闻国椿[1] 

机构地区：[1]北京大学数学学院,北京100871

出　　处：《吉首大学学报（自然科学版）》2006年第1期1-7,共7页Journal of Jishou University(Natural Sciences Edition)

基　　金：TheNationalNaturalScienceFoundationofChina(10471149)

摘　　要：讨论了带抛物退化线的二阶混合型(椭圆-双曲型)方程的间断斜微商边值问题.先给出这个问题的提法和解的表示式,然后使用一种新的复分析方法,即在椭圆区域上使用复变函数,在双曲区域上使用双曲复函数,最后证明了上述混合型方程间断斜微商问题解的存在性.The paper deals with the discontinuous oblique derivative problems for second order linear equations of mixed （elliptic-hyperbolic） type with parabolic degeneracy, which include the discontinuous Tricomi problem for Chaplygin equation as a special case. Firstly the formu- lation and representation of solutions of the above boundary value problems are given, and then the existence of solutions for the above problems is proved, in which the complex analytic method is applied, namely the complex functions in the elliptic domain and the hyperbolic： complex functions in hyperbolic domain are used.

关 键 词：间断斜微商边值问题 二阶混合型方程 抛物退化线 

分 类 号：O175.2[理学—数学]