How does the traffic flow model arrive at the scaled equation?
Consider the model for traffic flow with density $ρ(x, t)$ that satisfies
$ρ_t + (ρV_*(1 − ρ/ρ_*))_x = 0$
where $V_*$ was a given maximum speed and $ρ_*$ a given maximum density. Show that by scaling $ρ$ and a combination of $x$ (space) and $t$ (time) we can arrive at the scaled equation
$u_t + (u − u^2)_x = 0$
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