个端点自由 2)(x,D)=0 (0<x<∞ 设初始条件为4=0=0(x)和u1|=0=v(x) 边界条件 uxx=0 =0 应该是偶延拓cmy=/mx)(x20) (x≥0) (x) (-x (x< (x< l(x,)=[d(x+a)+Φ(x-a)]+ H(2d5 2 Lo(x+at)+o(x-at)+ v()d5 (t≤x/a) u(x,t) Lo(x +at)+o(at-x)]+ ∫v(5)5+∫ v(d(t≥x/a) a 2 (t≥x/a) H()d5 H()d5 H()d5 l y(5d5 (-5)d5 x-ar Y-ar ()d y(-5)d(-5) 2aw(5)d5+ 2a了v(5)d(5)一个端点自由 ( ) ( , ) 0 2 2 2 2 2 =   −   u x t x a t (0  x  ) 设初始条件为 ( ) 0 u x t= = 和 ( ) 0 u x x t= = 边界条件 ux x=0 = 0 应该是偶延拓    −    = ( ) ( 0) ( ) ( 0) ( ) x x x x x      −    = ( ) ( 0) ( ) ( 0) ( ) x x x x x    d a u x t x at x at x at x at ( ) 2 1 [ ( ) ( )] 2 1 ( , ) =  + + − +   + −        + + − + +  + + − +     + − + − ( ) ( / ) 2 1 ( ) 2 1 [ ( ) ( )] 2 1 ( ) ( / ) 2 1 [ ( ) ( )] 2 1 ( , ) 0 0 d t x a a d a x at at x d t x a a x at x at u x t x a t a t x x a t x a t              ( ) ( ) 2 1 ( ) 2 1 ( ) ( ) 2 1 ( ) 2 1 ( ) 2 1 ( ) 2 1 ( ) 2 1 ( ) 2 1 ( ) 2 1 ( / ) 0 0 0 0 ( ) 0 0 0 0                         d a d a d a d a d a d a d a d a d a t x a x a t a t x x a t x a t x a t x a t x a t x a t x a t x a t          + − − − + − + − + + − = − − − = +   =  +  = + −