On the uniqueness of semi-wavefronts for non-local delayed reaction–diffusion equations

Abstract

We establish the uniqueness of semi-wavefront solution for a non-local delayed reactiondiffusion equation. This result is obtained by using a generalization of the Diekman-Kaper theory for a nonlinear convolution equation. Several applications to the systems of non-local reaction-diffusion equations with distributed time delay are also considered.

On existence of semi-wavefronts for a non-local reaction–diffusion equation with distributed delay

“…As it was obtained in [1], ψ satisfies In this way, let c * and c be the minimal value of c for which χ 0 (z, c) = 0 and χ L (z, c) = 0 have at least one positive root, respectively. Then we can now formulate the following result: Theorem 5.2.…”

“…In [1] we have proved that for any c < c * the equation (2.1) has no semi-wavefront solution propagating with speed c vanishing at −∞. Remark 4.5.…”

“…Since the process developed in [1] to obtain (5.3) and (5.4) is invertible, it follows that (φ(t), ψ(t)) is a semi-wavefront solution to (5.2) propagating with speed c. In consequence we have the following theorem.…”