C.解 v(xt x=0 v(x,)x==0 -=/(x0 u(x, t=v(x,t; r)dr 数学检验: 边界条件:70=0 u"(x, dl=vx, t; r),dr=0 初始条件 vdt=0 u'l=0=lim u".(x, ) =lim a v(, t; r)dr tC. 解 0 2 vtt − a vxx = v(x,t) x=0 = 0 v(x,t) x=l = 0 0 v t= +0 = ( , ) 0 v f x t t t= + =  = t II u x t v x t d 0 ( , ) ( , ; )  数学检验： 边界条件： ( , ) ( , ; ) 0 0 0 = 0 = =  = t x x II u x t v x t  d ( , ) ( , ; ) 0 0 = = =  = t x l x l II u x t v x t  d 初始条件 0 0 0 0  u t= = vd = II lim ( , ) 0 0 u u t x t II t t t II → = =    = → t t v x t d t 0 0 lim ( , ; ) 