Forced waves of time-delayed nonlocal dispersal equations in shifting habitats

Abstract

To investigate the combined effects of time delay, nonlocal dispersal and climate change on population dynamics, we consider a time-delayed nonlocal dispersal equations in shifting habitats. Firstly, with the construction of appropriate lower and upper solutions, the existence of forced waves is established via the monotone iteration scheme. Furthermore, we show that the forced wave profile is unique in the classic sense, i.e., NOT up to a shift in the co-moving frame coordinate, by applying the sliding technique. Our result shows that time delay does not prevent the occurrence of forced extinction waves for non-locally diffusive populations in degraded habitats.