Propagation dynamics of an anisotropic nonlocal dispersal equation with delayed nonlocal response

Abstract

This paper focuses on the critical wave speed and the traveling wave fronts for a general anisotropic nonlocal dispersal equation with delayed nonlocal response. Unlike most of the previous study, both of the dispersal kernel function and the nonlocal response function are asymmetric in such an equation. By analyzing the properties of eigenfunction, we first discuss the sign of the critical wave speed and the influence of the asymmetry of the two kernel functions on the critical wave speed. Then under the monostable condition, by using super- and subsolution and monotone iteration method, we obtain the existence of nondecreasing traveling wave solution for c>c∗ and a limiting argument for c=c∗. Moreover, we depict the asymptotic behavior of the traveling wave and its derivative at minus infinity.