各向异性电介质无界域泊松方程的定解问题

Explicit Solution to Unbounded Domain Poisson Equation in Anisotropic Dielectric

陈燊年推导出了各向异性电介质静电势泊松方程的δ函数形式,但未将其应用于各向异性电介质无界域泊松方程的定解问题上。文章以求解点电荷在无限大导体平面上方各向异性电介质中激发的电势分布为例,由各向异性电介质静电势泊松方程的δ函数形式出发,应用联合积分变换法求解各向异性电介质无界域泊松方程的定解问题。

Chen Shennian deduced Poisson equation in anisotropic dielectric with delta function for electrostatic potential,but he did not apply it to explicit solution to unbounded domain Poisson equation in anisotropic dielectric.Taken the potential distribution of point charge excitation in anisotropic dielectric above the plane of infinite conductor as an example,the joint integral transformation method was applied to solve the problem of unbounded domain in anisotropic dielectric in order to provide the application supplement for explicit solution to unbounded domain Poisson equation in mathematical.