Precise propagation dynamics of the nonlocal KPP free boundary problem with non-symmetric kernels

This talk presents our recent joint work with Professor Yihong Du and Professor Xiangdong Fang on the asymptotic limit of the principal eigenvalue of asymmetric nonlocal diffusion operators and its implications for propagation dynamics in Fisher–KPP type equations. We first establish an explicit formula for the asymptotic limit of the principal eigenvalue of a nonlocal diffusion operator with drift, revealing how the asymmetry of the dispersal kernel affects the spectral structure. Building on this result, we analyze the long-term behaviour of nonlocal KPP equations using an eigenvalue-based approach that avoids the reliance on traveling waves.