= Viscous Burgers step solution with negative flux
{title2=$f=U/(1+Je^{-U(2\theta+UZ)/(4\alpha)})$}
For positive diffusivity, the <Cole-Hopf transformation> with $f=2\alpha\partial_\theta\log\psi$ converts the negative-flux equation into the <heat equation>. Step data give a ratio of two Gaussian-tail integrals $J$. At $\theta=-UZ/2$, $J=1$ and $f=U/2$. Its <vanishing-viscosity limit> selects the shock or <rarefaction wave> in the <Burgers Riemann problem with negative flux>, depending on the sign of $U$.
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