我們探討橢圓偏微方程Lu º -e Du + pux + guy + qu = f ,在四方形W = (0,a) ´ (0, b) 上的Dirichlet邊界值問題，其中0< e <<1，D是Laplacian運算，而且p, g,q 和f 滿足某些假設；特別是p>0, q ³ 0。對很小的e ，我們構造這個問題的解的一個形式的漸近展開。這個展開式包含退化方程的解和邊界層函數。拋物線邊界層函數滿足一個拋物線方程，其具有一個無界的係數。我們轉換此拋物線方程成一個熱方程，以此來討論拋物線邊界層函數的性質。最後這個展開式的剩餘項被估計為e 的次方。

where 0 < ε « 1, Δ is the Laplacian operator, and the functions p, g, q and f satisfy certain hypotheses;in particular, p > 0, q ≧ 0. We construct a formal asymptotic expansion of the solution u of this problemfor small ε. This expansion contains the solution of the reduced equation and boundary layer functions.The parabolic boundary layer functions satisfy a parabolic equation with an unbounded coefficient. We
transform the parabolic equation into a heat equation to develop properties of the parabolic boundary layer.Estimates for the remainder in the expansion are established that are of the order of magnitude of powers
of ε.