 Stellar mass in a constant-inflow gas regulator

For initially no stars, $M_{\star }=\Phi t+(M_0-\Phi /ϵ)(1-e^{-ϵt})$. Adding the gas solution verifies $M_g+M_{\star }=M_0+\Phi t$. Thus equilibrium of the gas reservoir coexists with continuing linear growth of stellar mass.