Spreading Properties of Partially Degenerate Diffusive Systems in Shifting Environments

ABSTRACT This paper investigates the spreading properties of partially degenerate reaction–diffusion systems in shifting environments. First, we study the propagation dynamics of a coupled system derived from a sugar beet agro‐ecosystem. To analyze its traveling wave solutions starting from the trivial steady state, the corresponding initial value problem is considered. By constructing appropriate upper and lower solutions and using the properties of the corresponding Cauchy problem, we establish the existence and nonexistence of two distinct types of traveling wave solutions. As an application of our recipe, we also present the spreading speeds of a partially degenerate delayed SIR model in a shifting environment.