报告题目：Wavefronts for a nonlinear nonlocal bistable reaction-diffusion equation in population dynamics
邀请人： 刘君 副教授
报告摘要：In this talk we study a nonlinear nonlocal reaction-diffusion equation which arises in population dynamics with nonlocal consumption of resources. The local version of this problem is the so called Huxley equation. It has three constant solutions, 0, a and A. It's proved that there exists a minimum speed such that the traveling waves connecting a and A exist for all values of the speed greater than or equal to this minimum speed. While the traveling waves connecting 0 and A exist only for a single value of the speed.In this talk, after reviewing the results for the nonlocal Fisher-KPP reaction diffusion equations, we will show the existence of wavefronts for the equation with nonlocal competition term, for which the most challenging point arises from the lack of the comparison principle. Firstly by monotone iteration method, we establish the existence of monotone wavefronts connecting the two positive equilibrium a and A. Next, we prove the existence of semi-wavefronts by a limiting process. Moreover, for $/sigma$ sufficiently small, we prove that the semi-wavefronts are wavefronts connecting 0 and A. Furthermore, as $/sigma$ goes to zero, we prove that the wavefronts converge to those of the corresponding local problems. This is a joint work with Li Chen and Evangelos Latos.