 Outflow boundary layer

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