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

Abstract

In a rectangular domain the first boundary value problem is considered for a singularly perturbed elliptic equationε 2∆u − ε αA(x, y) ∂u/∂y = F(u, x, y, ε)with a nonlinear on u function F. The complete asymptotic solution expansion uniform in a closed rectangle is constructed for α > 1. If 0 < α < 1, the uniform asymptotic approximation is constructed in zero and first approximations. The features of the asymptotic behavior are noted in the case α = 1 .

Keywords

• пограничный слой
• сингулярно возмущенное уравнение
• асимптотическое разложение решения