Morphogen source-diffusion-degradation model ($\lambda =\sqrt{D/k}$)

An idealized model balancing localized production, diffusion and degradation. In one dimension at steady state, away from the source, $D{c}^{\prime \prime }-kc=0$ gives $c(x)=c_0{e}^{-x/\lambda }$ with $\lambda =\sqrt{D/k}$. Tissue geometry and time-dependent source distributions can invalidate a simple point-source interpretation.