Toronto Math Forum

APM346-2016F => APM346--Lectures => Chapter 2 => Topic started by: Shaghayegh A on September 25, 2016, 03:41:49 PM

Title: derivation of a PDE describing traffic flow
Post by: Shaghayegh A on September 25, 2016, 03:41:49 PM
In example 8 of chapter 2.1 where we derive a PDE describing traffic flow, how do we derive $ρ_t+vρ_x=0\;(6)$ from $p_t+q_x=0\;(3)\;?$

It seems that $q_x$ some how equals $vp_x=[c(\rho)+ c' (\rho)\rho] \;p_x=c(p) \frac{\partial p}{\partial x}+\frac{d c(p)}{p} p \frac{\partial p}{\partial x}$? Can someone please explain how we get equation (6)? Thanks
Title: Re: derivation of a PDE describing traffic flow
Post by: Victor Ivrii on September 26, 2016, 05:45:03 AM
You plug $q= q(\rho)$ into $\rho_t + q_x=0$