= Interior layer at a simple zero of advection
{title2=$z=(x-x_*)/\varepsilon$}
In $\varepsilon^2y''+a(x)y'+\cdots=f$, a simple zero $a(x_*)=0$, $a'(x_*)\ne0$, balances diffusion and advection on width $\varepsilon$. With $a(x)\simeq2(x-x_*)$, the leading homogeneous inner equation is $Y''+2zY'=0$, whose bounded solutions are constants and the <error function>. Thus distinct order-one <outer solutions> can match across an interior transition. Reversing the diffusion sign makes the nonconstant homogeneous solution grow at both ends, changing the matching structure.
Back to article page
