Solve the Riemann Problem
Consider the Riemann Problem (RP) for the traffic flow model
$u_t + (u − u^2)_x = 0$
$U_L = 5/6$ and $U_R = 1/2$
i) Solve the RP. It will have a rarefaction wave.
ii) In the model,
$(u − u^2)/u = 1 − u$
(flux divided by density) is the scaled average speed of an individual car. Find the formula for the position $x(t)$ of a car that starts at $x(0) = −1$ in the traffic described by the RP above. Hint: it will be a three part solution, with two easy parts.

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 Attachment
1.6K
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
- 737 views
- $13.00
Related Questions
- Lyapuniv-functions
- Differential Equations (2nd-order, general solution, staionary solution, saddle point, stable branch)
- Derive the solution $u(x,t)=\frac{x}{\sqrt{4 \pi}} \int_{0}^{t} \frac{1}{(t-s)^{3/2}}e^{\frac{-x^2}{4(t-s)}}g(s) \, ds$ for the heat equation
- Can someone translate $s_j : \Omega \hspace{3pt} x \hspace{3pt} [0,T_{Final}] \rightarrow S_j \subset R$ into simple English for me?
- Long time behavior of solutions of an autonomous differential equation
- Optimisation Problem
- How to determine the stability of an ODE
- Week solution of the equation $u_t + u^2u_x = f(x,t)$