Square-root boundary layer at a vanishing drift
= Square-root boundary layer at a vanishing drift
{title2=$z=x/\sqrt\varepsilon$}
In $\varepsilon y''+2xy'-2xy=0$, the drift vanishes at the endpoint $x=0$. Balancing diffusion against drift gives the <inner expansion> coordinate $z=x/\sqrt\varepsilon$. The leading layer equation is $Y''+2zY'=0$, with a bounded <error function> profile. A regular outer first-order calculation alone cannot impose both endpoint values.