Corner Boundary Layer in Nonlinear Elliptic Problems Containing First-Order Derivatives

摘要

In a rectangular domain, the first boundary-value problem is considered for the following singularly perturbed elliptic equation: ε~2Δu - ε~ΔA(x, y){partial deriv}u/{partial deriv}y = F(u, x, y, ε) with the function F, which is nonlinear in u. The complete asymptotic solution expansion, which is uniform in a closed rectangle, is constructed for Δ > 1. If 0 < Δ < 1, the uniform asymptotic approximation is constructed as a zero and first approximation. The features of the asymptotic behavior are noted at Δ = 1.