高阶复偏微分方程的两类边值问题

兰州理工大学学报 ›› 2024, Vol. 50 ›› Issue (5): 161-164.

高阶复偏微分方程的两类边值问题

崔艳艳^*, 王朝君

周口师范学院数学与统计学院, 河南周口 466001

收稿日期:2023-03-09 出版日期:2024-10-28 发布日期:2024-10-31
通讯作者: 崔艳艳(1981-),女,河南确山人,博士,副教授.Email:cui9907081@163.com
基金资助:
国家自然科学基金(11601543),河南省自然科学基金(222300420397),河南省教育厅科学技术研究重点项目(19B110016),河南省科技厅软科学项目(102400450003)

Two classes of boundry value problems for higher-order complex partial differential equations

CUI Yan-yan, WANG Chao-jun

College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China

Received:2023-03-09 Online:2024-10-28 Published:2024-10-31

摘要/Abstract

摘要： 利用C中的Gauss定理和Cauchuy-pompeiu公式,讨论单位圆盘上关于高阶复偏微分方程的Dirichlet问题和Neumann问题,从而得到解的积分表示和相应的可解条件,并由此得到关于多全纯函数边值问题的相关结论.

关键词: 全纯函数, 边值问题, 偏微分方程

Abstract: By the Gauss theorem and Cauchuy-pompeiu formula in C, the Dirichlet problem and Neumann problem for higher order complex partial differential equations on the unit disc are discussed, and the integral representations and the conditions of the solutions are obtained, which lead to the conclusion of the boundary value problem for poly-analytic functions.

Key words: holomorphic functions, boundary value problems, partial differential equations

中图分类号:

O174.56

崔艳艳, 王朝君. 高阶复偏微分方程的两类边值问题[J]. 兰州理工大学学报, 2024, 50(5): 161-164.

CUI Yan-yan, WANG Chao-jun. Two classes of boundry value problems for higher-order complex partial differential equations[J]. Journal of Lanzhou University of Technology, 2024, 50(5): 161-164.

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