Asymptotic patterns of a reaction-diffusion equation with nonlinear-nonlocal functional response

摘要

A reaction-diffusion system with nonlinear-nonlocal functional response is considered in this article. We develop the finite delays approximation method combining with the spreading speed and travelling wavefronts theory for semi-flow to discuss the existence of spreading speed c~* and travelling wavefronts without the differentiability assumption on the reaction function f. The asymptotic patterns and threshold property for the solutions of the considered system are described clearly according to the threshold parameter c~* which is exactly the minimal wave speed as well. Finally, we give an estimate of the spreading speed and minimal wave speed c~*.