Fourier transform for the steady problems Solving the steady problems urr+uw=0, y>0 l(x,y)→U(k,y) k2U=0 0(x)→>d(k) l=0=0(x) U y=0 y→> u=U(k, y)e dk ds l=0(s) Jy U=exp(k y Tx-s)+yFourier Transform for the steady problems        = =  − = → = | 0 | 0 0 2 y y yy U U U k U [( ) ] ( ) 2 2 x s y yds u s − + =    Solving the steady problems      = = + =  → = | 0 | ( ) 0, 0 0 y y xx yy u u x u u y  U = exp(− | k | y) ( ) ( ) ( , ) ( , ) x k u x y U k y →  →   u = U k y e dk ikx ( , )