/ f.+ ( 0( : Xn(x; x )/f.} )(1 x 1. Thus, up to terms of order m Xn(O; fn, Xn(1;

doi:10.1201/b16933-11

ABSTRACT

Note also that under condition (16) the functions Xn(x;E)sin(mry) with Xn as given by (9) satisfy the reduced equation (5). That is, this range of Fourier coefficients of f produces parabolic layers. When j(2k)(y) f; 0 at y = 0 or y = 1 for some even-order derivative, we get a parabolic boundary layer, while nonsmoothness off in the interior of the interval 0 < y < 1 produces parabolic internal layers.