Propagation dynamics of a discrete diffusive equation with non‐local delay

Abstract

This paper is concerned with the propagation dynamics of a discrete diffusive equation with non‐local delay. First of all, by exploring the asymptotic behavior of the solution of the upper system corresponding to the perturbation equation, we obtain the global stability of semi‐wavefronts. It is noteworthy that the kernel function can be asymmetric (i.e., ). Secondly, we estimate the level set of the equation on the basis of the above stability. In particular, the results show that the solution of the compact supported initial value problem is not persistent in special case.