| 许景生.各向异性电介质二维无限域拉普拉斯方程定解问题[J].海南师范大学学报自科版,2020,33(2):198-205 |
| 各向异性电介质二维无限域拉普拉斯方程定解问题 |
| Explicit Solution to Two-dimensional Infinite Domain Laplace Equation in Anisotropic Dielectric |
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| DOI：10.12051/j.issn.1674-4942.2020.02.013 |
| 中文关键词: 各向异性电介质 拉普拉斯方程 分离变量法 傅里叶变换 |
| 英文关键词: anisotropic dielectric Laplace equation separate variable Fourier transformation |
| 基金项目: |
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| 摘要点击次数: 816 |
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| 中文摘要: |
| 分别应用分离变量法和傅里叶变换法求解各向异性电介质二维无限域拉普拉斯方程
的定解问题。所得的解有两种不同的数学形式，分离变量法求得的解是用傅里叶积分表示的，傅
里叶变换法求得的解是用傅里叶卷积表示的。由静电场的唯一性定理可知，虽然这两种解有不同
的数学表达式，但具备等价性。文章还列举典型算例间接验证了这两种解的等价性，并给出了相
应的各向异性电介质物理模型。 |
| 英文摘要: |
| The separation variable method and the Fourier transform method were used in the explicit solution to two-di‐
mensional infinite domain Laplace equation in anisotropic dielectrics respectively. The solution obtained by the separation
variable method was expressed by the Fourier integral, and the solution obtained by the Fourier transform method was ex‐
pressed by the Fourier convolution. According to the uniqueness theorem of the electrostatic field, although these two kinds
of solutions have different mathematical expressions, they should be equivalent. The equivalence of the two solutions was in‐
directly verified by typical examples, and the corresponding anisotropic dielectric physical models were given. |
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