Asymptotic speed of propagation and traveling wave solutions for a lattice integral equation

Traveling waves in a convolution model with infinite distributed delay and non-monotonicity

“…Due to its natural background and applicable potential in physics, biology and epidemics, the theory of traveling wave solutions has been extensively developed in the literature (see [1][2][3] and the references therein) since the pioneer work of Fisher [4] and Kolmogorov et al [5]. The studies include the existence, non-existence, minimal wave speed, uniqueness and stability of traveling wave solutions etc., and also involve more extensive dynamical properties such as the asymptotic speed of propagation (see [6][7][8][9]).…”

Threshold asymptotic behaviors for a delayed nonlocal reaction-diffusion model of mistletoes and birds in a 2D strip

“…The research for spreading speed can be traceable from Aronson & Weinberger [1] for reaction-diffusion systems and Weinberger [18] for recursion systems, and also can be found in references for many types of evolutionary systems (e.g. see [3,8,12,13,14,20,21,22,23,24,26]). Spreading speed c * is in fact a threshold value, the existence of which reveals the different asymptotic patterns as time t → ∞, while the wave speed parameter c crosses c * , generating two unbounded sub-domain for solution spreading (see details in Theorem 5.3).…”