上游充大 SHANGHAI JIAO TONG UNIVERSITY 川类齐次边界条件 4,=a24u, 0<x<1,t>0 u(0,t)=0=w(l,t)+hu(l,t),t>0 u(x,0)=p(x), 0≤x≤1 解: u(x,t)=X(x)T(t)代入PDE和边界条件, 固有问题 X"+X=0 0<x<1 X(0)=0, X'()+hX()=0 入≤0,无非零解. T'+a2T=02 T aT ′ + = λ 0 0 0 (0) 0, ( ) ( ) 0 X X xl X X l hX l ′′ + = << λ = += ′ III类齐次边界条件 解: λ ≤ 0, 无非零解. 2 , 0 ,0 (0, ) 0 ( , ) ( , ), 0 ( ,0) ( ), 0 t xx x u au x lt u t u l t hu l t t ux x φ x l = << > == + > = ≤ ≤ (I) u xt X xT t ( ,) ( ) () = 代入PDE和边界条件, (II) 固有问题