Selection at the pushed-to-pulled transition

Let $u_\mathrm{tr}$ be a pushed-to-pulled transition front. A pushed-to-pulled transition front is a front at the boundary between pushed and pulled invasion, characterized here by the marginal stability conditions described in the surrounding discussion. Selection at the pushed-to-pulled transition. $u_\mathrm{tr}$ should be a selected front, with position correction

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

Selection at this transition is known for scalar second-order equations using comparison principles, while the analogous result for systems remains open; uniform asymptotics across the pushed-to-pulled transition are also open.