= Sonic point of a scalar flux
{title2=$f\prime(s_*)=0$}
= Stagnation point of a scalar flux
{synonym}
For a differentiable <scalar conservation law> $u_t+f(u)_x=0$, a <sonic point of a scalar flux> is a state $s$ where its <characteristic speed> $f'(s)$ vanishes. If $f$ is convex and this zero is unique, $f'<0$ on the left and $f'>0$ on the right, so $s$ is the unique minimum of the flux. The definition refers to a vanishing transport speed in a <scalar conservation law>. In compressible <fluid mechanics>, a <sonic point> instead refers to flow at the local sound speed.
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