具有卷积核的奇异积分方程与Riemann边值问题  

The Singular Integral Equations with Convolution Kernel and Riemann Boundary Value Problems

作　　者：李平润[1] 

机构地区：[1]曲阜师范大学数学科学学院,山东曲阜273165

出　　处：《工程数学学报》2014年第2期245-253,共9页Chinese Journal of Engineering Mathematics

基　　金：曲阜师范大学校青年基金(XJ201218)~~

摘　　要：本文首次提出并研究了在指数增长的函数类中,含卷积核和Cauchy核的奇异积分方程,特别就对偶型的奇异积分方程进行了讨论与求解,利用Fourier变换以及本文给出的引理,把对偶型奇异积分方程转化为直线上或平行直线上的解析函数边值问题.本文采用与经典的边值问题不同的解法,得到了方程的可解条件与一般解,因此推广了卷积型奇异积分方程理论,并为解决有关物理问题提供了理论依据.In this paper, one class of singular integral equations with convolution kernel and Cauchy kernel is studied firstly in the function class of exponential order increasing. Especially, by applying the Fourier transformation and lemmas given in this paper, the numerical method of dual type equation is discussed, and the singular integral equation of dual type is transformed into the Riemann boundary value problem in parallel lines. The proposed method is different from the classical boundary value problems. Thus, the general solution and the solvability condition are derived, which improve the theory of the singular integral equations of convolution type, and supply theoretical basis for solving relatively physics problems.

关 键 词：奇异积分方程 RIEMANN边值问题 对偶型 指数增长的函数类 标数 

分 类 号：O175.8[理学—数学] O175.5[理学—基础数学]