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
- 761 views
- $13.00
Related Questions
- Optimisation Problem
- Differential Equations
- 3 Multi-step response questions
- Differentai equations, question 2.
- Diffrential Equations
- Differential equations
- The domain of a solution and stability of solutions of a differential equation.
- 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