13. P236 L.-a2△u=0 () u(p=0)=finite v(z=0)=0(z=D)=2L4(t=0)=6 解 1分离变量=XTX-a27AX=0 T"+a2k2T=0△X+k2X=0 X=X+X △X1+kX1=0 △X,+k2X,=0 X1(p)=412 H1(x=0)=0,X1(==L)=0X2(x=0)=0,X2(==D)=2L TX1(t=0)=l xX2(t=0)=013. P.236 解 2 0 1 u( ) = u z 2 1 u(z = 0) = 0,uz (z = L) = Lu 0 u(t = 0) = u u( = 0) = finite 0 2 ut − a u = X = X1 + X2 1.分离变量 u = XT ' 0 2 XT −a TX = ' 0 2 2 T +a k T = 0 2 X + k X = 1 0 2 X1 + k X = 2 0 2 X2 + k X = 2 1 0 1 X ( ) = u z X1 (z = 0) = 0, X1 (z = L) = 0 1 0 TX (t = 0) = u X2 (0 ) = 0 2 2 2 1 X (z = 0) = 0, X z (z = L) = Lu TX2 (t = 0) = 0