Constant-temperature lava-crust growth law ($S{R}^2\tau =-Rh-\log (1-Rh)$)

In the radiogenically heated lava-lake crust model, temperature stays constant precisely when ${\theta }_0=R/B$. Then $h^{\prime }=S(1/h-R)$, and an initially absent crust satisfies the displayed law for $0\le h<1/R$. It follows by integrating $h/(1-Rh)$ from zero to $h$. The crust starts as $\sqrt{2S\tau }$ and tends to $1/R$ only at infinite time. The equilibrium remains thin only if $R\gg 1$.