Selection of rigid pulled pattern-forming fronts

Let $u_\mathrm{pl}$ be a rigid pulled pattern-forming front, meaning a rigid front with marginal spectral stability that leaves behind a diffusively stable periodic pattern and has negative group velocity. Selection of rigid pulled pattern-forming fronts. $u_\mathrm{pl}$ should be a selected front, with position correction

$$h(t)=-\frac{3}{2\eta_\mathrm{lin}}\log t+\mathrm{O}(1).$$

Rigorous selection remains open; partial results provide speed bounds and stability under perturbations that do not cut off the front tail.