Asymptotic analysis of the Carrier-Pearson problem

Abstract

This paper provides a rigorous analysis of the asymptotic behavior of the solution for the boundary-value problem begin{gather*} epsilon ^2u''+u^2-1 =0,quad -1<x<1, u(-1) =u(1)=0 end{gather*} as the parameter $epsilon$ approaches zero.

Keywords

• Boundary layers
• interior layer
• transcendentally small terms.