A Generalized Principal Eigenvalue Approach to Spreading Speeds for Time‐Heterogeneous Nonlocal Diffusion Models

Abstract

In this paper, we develop a unified framework based on generalized principal eigenvalues to study spreading speeds in time‐heterogeneous nonlocal diffusion models. First, for time‐heterogeneous environments with a positive uniform mean value, we investigate the properties and interrelationships of three types of generalized principal eigenvalues and establish sign criteria for them. Next, we use these signs to select appropriate test functions and explicitly construct upper and lower solutions on unbounded domains, thereby characterizing spreading speeds in two scenarios. One concerns a Fisher‐KPP equation with compactly supported initial data, and the other involves predator–prey systems with Holling‐type I–III functional responses, considering both coinvasion and predator‐invasion initial data. Overall, this framework offers an alternative perspective for quantifying the spatiotemporal evolution of solutions.