= Gaussian interior layer of a conservative drift equation
{c}
{title2=$y(x)=A\exp[(1-x^2)/(2\epsilon)]$}
The equation $\epsilon y''+xy'+y=0$ integrates to $\epsilon y'+xy=C$. Equal endpoint data $y(-1)=y(1)=A$ force $C=0$ and give the unique Gaussian solution above. Its central width is $\sqrt\epsilon$, with amplitude $A e^{1/(2\epsilon)}$. The exponentially large central mode is missed by an assumed bounded algebraic <outer expansion> $C/x$. Changes of order one relative to either endpoint value occur over distance $O(\epsilon)$ from that endpoint.
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