# Solve the Riemann Problem

$u_t + (u − u^2)_x = 0$

$U_L = 5/6$ 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.

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

1 Attachment

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- answered
- 185 views
- $13.00

### Related Questions

- Partial differential equations help
- Leaky Buckets: Volume in a system of 2+ buckets that can be empty
- Please solve this question
- Differential equations, question 3
- Linear solutions, linear systems, autonomous systems, and key points.
- Diffrential Equations
- A linear ODE
- Solve $Lx = b$ for $x$ when $b = (1, 1, 2)^T$.