Joint angular–resistance transition in the strong-resistance limit

Determine the angular scale and limiting profile governing the joint limit in which the interface resistance tends to infinity while the receiving direction approaches the equator, and control the Robin difference mode over the time range responsible for the logarithmic input tail.

Background

For every fixed receiving angle away from the equator, the strong-resistance asymptotics give a diverging arrival-time delay, whereas the equatorial strong-resistance limit is finite. The paper establishes the two iterated limits but not their joint behavior when the resistance and the normal component of the direction vary simultaneously.

Resolving this problem would identify the transition scale between the fixed-angle and exactly tangential regimes and would require estimates for the Robin difference mode over the long time interval generating the logarithmic input contribution.

References

The first is the joint limit in which $\beta\to\infty$ and $\theta_N\downarrow0$. The divergence of the delay at each fixed receiving angle, together with its finite equatorial limit, indicates a transition between these regimes. The iterated limits established here determine neither the angular scale of this transition nor its limiting profile.

— Directional delays and singular strong-barrier limits for Fisher--KPP propagation across a semipermeable interface  (2610.21328 - Wang, 15 Oct 2026) in Section 6, Further questions

The angular regularity of the amplitude also remains to be clarified beyond the H\

— Directional delays and singular strong-barrier limits for Fisher--KPP propagation across a semipermeable interface  (2610.21328 - Wang, 15 Oct 2026) in Section 6, Further questions