= Solution
At <equilibrium> $Q_s=M$, so $Q=Q_{\rm in}+Ms$ for an upstream boundary <flux> $Q_{\rm in}$. Hence
$$
\boxed{A_{\rm eq}(s)=\left[\frac{m+1}{c}(Q_{\rm in}+Ms)\right]^{1/(m+1)}.}
$$
Without a specified upstream condition this <integration> constant must be retained. On a region of positive <area>, the <characteristic> <speed> is $Q'(A)=cA^m>0$, increasing downstream along the <equilibrium>. Small disturbances move downstream, spread in space as this <speed> increases, and decrease in <area> <amplitude> in the manner derived next. They are transported away from a fixed location; the model has no <diffusion> giving instantaneous smoothing. Finite-amplitude compressive disturbances can steepen into shocks because the <flux> is <convex>, $Q''(A)=cmA^{m-1}>0$, so the small-disturbance picture is not a global no-shock assertion.
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