|
|
一类复偏微分方程边值问题的积分解
|
Abstract:
本文研究了周期平面上一类复偏微分方程边值问题，我们首先给出了周期平面上的Cauchy-Pompeiu公式。然后用这个公式给出原问题解的积分表示。
In this paper, a class of boundary value problems for complex partial differential equations on periodic planes is studied. We first give the Cauchy-Pompeiu formula on the periodic plane. This formula is then used to give the integral representation of the original solution.
| [1] | 王亚光. 偏微分方程——经典数学与现代数学的相互交融[J] . 世界科学, 2001(7): 24-25. |
| [2] | Muskhelishuili, N.I. (1958) Singular Iniegral Equations. Wolters-Noordhoff, Groningen. |
| [3] | 维库阿, И.Н. 广义解析函数[M]. 中国科学院教学研究所偏微分方程组, 北京大学数学力学系函数论教研组, 译, 北京: 人民教育出版社, 1960. |
| [4] | Begehr, H. (1994) Complex Analytic Methods for Partial Differential Equations. World Scientific, Singapore.
https://doi.org/10.1142/2162 |
| [5] | Begehr, H. (2005) Boundary Value Problems in Complex Analysis. Boletín De La Asociación Matemática Venezolana, 12, 65-86. |
| [6] | Begehr, H. (2007) Basic Boundary Value Problems in Complex Analysis. Journal of Applied Functional Analysis, 2, 57-71. |
| [7] | 王莹, 段萍, 杜金元. 正实轴上的Riemann边值问题[J]. 中国科学: 数学, 2017, 47(8): 887-918. |
