Spreading properties for a predator-prey system with nonlocal dispersal and climate change

In this paper, we investigate the spreading properties for a predator-prey system with nonlocal dispersal and climate change. We are concerned with the case when the prey grow relatively rapidly at one side of the habitat and grow relatively slowly at another side of the habitat. We are interested in the effect of the climate change on the spreading speed of the predator and prey. In the case where the predator is faster than the prey, we show that the predator and the prey have the same leftward spreading speed and the same rightward spreading speed, respectively, which depend on c, the climate change speed, and $c_1^{⁎}(\pm \infty )$, the maximum and minimum speeds of the prey without predator. While in the case where the prey is faster than the predator, we find that the solution can form a multi-layer wave and the two species have different leftward spreading speeds and different rightward spreading speeds, which depend on c, $c_1^{⁎}(\pm \infty )$ and $c_2^{⁎}(\pm \infty )$, the maximum and minimum speeds of the predator when the density of the prey attains its maximum and minimum capacity.