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
$u_t + (u − u^2)_x = 0$
![Chdogordon](https://matchmaticians.com/storage/user/100462/thumb/AOh14Gjz6akTt1aFMoa7ItCxU-OqVA2e95TuSYj3cx70=s96-c-avatar-512.jpg)
153
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1.2K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 486 views
- $13.00
Related Questions
- Calculus - 2nd order differential equations and partial derivatives
- Solve the two-way wave equation
- Finding all real solutions of a linear ODE.
- Fixed points of analytic complex functions on unit disk $\mathbb{D}$
- Use the divergence theorem to derive Green's identity
- Beginner Differential Equations - Growth Rate Question
- Solve the initial value problem $(\cos y )y'+(\sin y) t=2t$ with $y(0)=1$
- Solve $Lx = b$ for $x$ when $b = (1, 1, 2)^T$.