上游充通大 SHANGHAI JIAO TONG UNIVERSITY u三p(x) u,a'uxx ulx=o=u 0. u=T(t)X(x) X(0)=X(L)=0 分离变量流程图 T1a2T)=X"1X=-元 T'+a2B2T=0 X"+B2X=0 T=Aexp(-a"B"t) X=sin Bx,.B=℉ 4=T(0X(x u=u(x,t) u=∑TXxut a uxx 2 = 0 | |0 x xl u u u | t=0= ϕ(x) = = = = u = T(t)X (x) X (0) = X (L) = 0 T'/(a T ) = X" / X = −λ 2 2 2 Ta T ' 0 + = β 2 X X " 0 + = β 2 2 TA a t = − exp( ) β sin , n l X x π = = β β u T (t)X (x) k = k k ) u = ∑Tk Xk u = u(x,t 分离变量流程图