= Power-law drift endpoint-layer classification
For $\epsilon y''+x^\alpha y'+y=0$ near zero, <dominant balance> gives a diffusion-drift layer of thickness $\epsilon^{1/(\alpha+1)}$ for $-1<\alpha<1$, with the reaction term negligible. At $\alpha=1$, all three terms survive on the scale $\sqrt\epsilon$. For $\alpha>1$, diffusion and reaction first balance on wavelength $\sqrt\epsilon$, while the drift damps the oscillation on the larger envelope scale $\epsilon^{1/(\alpha+1)}$. Removing the first derivative gives the envelope factor $\exp[-x^{\alpha+1}/(2\epsilon(\alpha+1))]$. For $\alpha\leq-1$, no shrinking algebraic diffusion layer of this regular bounded type is obtained.
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