= Half-line drift global relation
{title2=$\widehat u_0-e^{\omega t}\widehat u=G_1+(ik+\alpha)G_0$}
For the <advection-diffusion equation> $u_t=u_{xx}+\alpha u_x$ on $x>0$, the spectral <divergence form> uses $\omega=k^2-i\alpha k$ and factor $e^{-ikx+\omega t}$. With negative-exponential <Half-range Fourier transforms>, integration gives the displayed <global relation> for $\operatorname{Im}k\le0$. The boundary transform $G_1$ refers to $u_x(0,t)$, the negative of the outward <normal derivative>.
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