# How does the traffic flow model arrive at the scaled equation?

$ρ_t + (ρV_*(1 − ρ/ρ_*))_x = 0$

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

$u_t + (u − u^2)_x = 0$

Chdogordon

153

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Martin

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