Bounded-derivative Burgers flux ($f(z)=z^2/2(|z|\le 1),f(z)=|z|-1/2(|z|\ge 1)$)

This $C^1$ flux has $|f^{\prime }|\le 1$ globally and agrees with the Inviscid Burgers equation flux on $[-1,1]$. It allows Burgers examples to satisfy a global bounded-speed hypothesis. For Riemann data $-1$ to the left and $1$ to the right, both the stationary expansion discontinuity and the fan $u=x/t$ on $|x|<t$, with exterior values $\pm 1$, are bounded weak solutions. Only the fan is an entropy solution.