令:m(x1)=V(x,1)+W(x,D 原定解问题可作如下分解: L1V+LV=0,(t>0,x1<x<x2) a, V(t,x1)+B V(t,x1=0 a2Vx(t,x2)+B2(t,x2)=0 V(0,x)=(x),V7(0,x)=(x) 与 L,W+LW=f(x, t),(t>0,x,<x<x2) a1W2(t2x)+BW(,x)=0 a,W(t,x)+B,W(t,x,)=0 W(0,x)=0,W(0,x)=00.8 1 0.6 0.4 0.2 0 x t 0 0.5 1 1.5 2 −1 −0.5 0 0.5 1 n 6 1 2 1 1 1 1 2 2 2 2 0,( 0, ) ( , ) ( , ) 0 (1) ( , ) ( , ) 0 (0, ) ( ), (0, ) ( ) t x x x t LV L V t x x x a V t x V t x a V t x V t x V x x V x x      + =      + =  + =    = = 令： u x t V x t W x t ( , ) ( , ) ( , ) = + 与 原定解问题可作如下分解 ： 1 2 1 1 1 1 2 2 2 2 ( , ),( 0, ) ( , ) ( , ) 0 (2) ( , ) ( , ) 0 (0, ) 0, (0, ) 0 t x x x t LW L W f x t t x x x a W t x W t x a W t x W t x W x W x    + =      + =  + =    = =