Hi, I need a bit of help understanding what this question wants.

$\displaystyle (\frac{1}{2^5}u^4)_x + u_t =0$

1. How do I find the Rankine-Hugoniot shock speed condition for this?

EDIT: Got this:

$\displaystyle s=\frac{F(u_L)-F(u_R)}{(u_L-u_R)}$

2. How do I find the rarefaction fan for this such that $\displaystyle u(x,t)=g(x/t)$ is a solution.

Thank You for any help.