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

作者：Tian Yanling^*; Weng Peixuan

来源：IMA Journal of Applied Mathematics, 2013, 78(1): 70-101.

DOI：10.1093/imamat/hxr038

• reaction-diffusion system
• nonlinear-nonlocal functional response
• spreading speed
• travelling wavefront
• minimal wave speed

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*.

• 出版日期2013-2
• 单位华南师范大学