= Bounded-derivative Burgers flux
{title2=$f(z)=z^2/2\ (|z|\le1),\quad f(z)=|z|-1/2\ (|z|\ge1)$}
This $C^1$ flux has $|f'|\le1$ 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 $\pm1$, are bounded weak solutions. Only the fan is an <entropy solution>.
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