Abstract

This talk is devoted to studying the asymptotic spreading speed of a predator-prey system, in which predators on the straight line and those on the half plane diffuse differently. We give a sharp characterization of the spreading properties of solutions of the system with compactly supported initial values by appealing to the invasion speed of the prey when the predator is absent, and the invasion speed of the predator when the prey is saturated. Notably, since the line may accelerate the expansion of the predator in a cone of directions, the invasion speed of the predator varies with the direction. In this paper we first derive pointwise comparisons between the predator and prey and then reduce the components of predators in the system to a truncated field road system depending on the invasion speed of the prey. By using known results for the single-species field-road model, we further show the propagation properties of the truncated system. Once the propagation properties of the truncated system are established, we can obtain the expected spreading properties of solutions to the original system by applying the comparison principle and contradiction arguments, and constructing appropriate Lyapunov functionals.