= Biomass yield identity for a depletion front
{title2=$b_1=1-\frac\eta c\int_{\mathbb R}gb^2\,dy<1$}
With inhibited <bacteria>[bacterial] growth $b_t=b_{xx}+gb(1-\eta b)$ and unchanged depletion $g_t=-gb$, a positive <travelling wave> leaving <number density>[density] $b_1$ obeys $cb_1=c-\eta\int_{\mathbb R}gb^2\,dy$. This follows by <integral>[integrating] both <travelling wave>[travelling-wave equations] between their constant endpoint states. Thus $b_1<1$ for $\eta>0$: the yield behind the <travelling wave>[front] is smaller than for uninhibited growth.
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