Outflow boundary layer
= Outflow boundary layer
For $\epsilon y''+a(x)y'+b(x)y=0$ with $a>0$, the reduced first-order outer problem takes its boundary condition at the right endpoint. A rapidly decaying exponential in $x/\epsilon$ supplies the otherwise unsatisfied left-end condition, so the layer lies at the outflow end for the fast mode associated with this sign convention.