一类三维偏微分方程边值问题的解法

基于偏微分方程第三类边值问题，提出了一类同时包含第一类、第三类边界条件的边值问题，探讨了此类边值问题如何转化为变分与泛函极值问题．用三个定理证明了在一定条件下三者解之间的等价关系，拓宽了偏微分方程边值问题的求解思路．并灵活运用此三类问题，使复杂方程问题简单化．这不仅为数学、还为物理、生物、化学、计算机信息等各学科求解方程提供了捷径．

Solution to a class of boundary-value problem of three-dimensional partial differential equations

Based on the third class boundary value problem for three-dimensional partial differential (equations,) a new boundary value problem,which includes the first and third class boundary conditions, was proposed. The transformations from this class of boundary value problem to variational problem and functional extremal problem were discussed. By using three theorems the relationship among the three solutions was proven equal under certain conditions. Therefore, methods of solving the boundary value problem of partial differential equations are extended. In pratice, this method can simplify the difficult problems and provide shortcut for solving equations in mathematics, physics and mechanics.