变积分限Cauchy核与卷积核混合的完全奇异积分方程的求解

吉林大学学报(理学版)

变积分限Cauchy核与卷积核混合的完全奇异积分方程的求解

冯志新

吉林师范大学数学学院, 吉林四平 136000

收稿日期:2013-06-09 出版日期:2013-11-26 发布日期:2013-11-21
通讯作者: 冯志新 E-mail:fengzhixin2008@163.com

Solution of Complete Singular Integral Equation withCauchy and Convolution Kernels and Variable Limit

FENG Zhixin

College of Mathematics, Jilin Normal University, Siping 136000, Jilin Province, China

Received:2013-06-09 Online:2013-11-26 Published:2013-11-21
Contact: FENG Zhixin E-mail:fengzhixin2008@163.com

摘要/Abstract

摘要：

考虑{0}函数类中, 变积分限的Cauchy核与卷积核混合的完全奇异积分方程的求解问题, 借助Fourier积分变换, 利用Riemann边值问题和Fredholm积分方程理论, 先将所讨论的方程转化为在一定可解条件下与其等价的{{0}}类中的Fredholm积分方程, 再通过求解等价的Fredholm积分方程, 得到所研究方程在{0}函数类中的可解条
件及一般解.

关键词: 奇异积分方程, 卷积核, Cauchy核, Fredholm积分方程

Abstract:

We discussed the solution of complete singular integral equation with Cauchy and convolution kernels and variable limit. Based on the Fourier transform and the theory of Riemann boundary value problem and Fredholm integral equation, the equation was transfered to the equivalent Fredholm integral equation in {{0}} undering some conditions. Then solving the equivalent Fredholm integral equation, we got solvable conditions and general solution on the equation discussed in {{0}}.

Key words: singular integral equation, convolution kernel, Cauchy kernel, Fredholm integral equation

中图分类号:

O175.6

冯志新. 变积分限Cauchy核与卷积核混合的完全奇异积分方程的求解[J]. 吉林大学学报(理学版), 2013, 51(06): 1051-1057.

FENG Zhixin. Solution of Complete Singular Integral Equation withCauchy and Convolution Kernels and Variable Limit[J]. Journal of Jilin University Science Edition, 2013, 51(06): 1051-1057.

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