W(x,t)普遍结果的推导

The Derivation of the Universal Result of W (x,t)

用分离变量法求解数理方程定解问题时,要求其第一、二、三类边界条件必须是齐次的。若为非齐次的,必须寻求恰当的辅助函数w(x,t),进行变换,将其化为齐次的。从稳定条件下的线性非齐次边界条件出发,给出了w(x,t)的统一形式,进而将其推广到非稳定条件下的非齐次边界条件,得到w(x,t)的一般的结果。

When separation variable method is used to solve the fixed solution problem of mathematical equation, the boundary condition of its first, second and third type must be homogeneous. If they are unhomogeneous, proper supplementary function W (x,t) must be found to substitute, then they will be homogenized. In this paper, first, the unified form of W (x,t) is presented on the condition of linear unhomogeneous boundary condition under stable condition. Then, it can be extended into unhomogeneous boundary condition under unstable condition and the general result of can be obeained.