Traveling Fronts in Monostable Equations with Nonlocal Delayed Effects

On the minimal speed of traveling waves for a nonlocal delayed reaction–diffusion equation

“…It is known [9] that for various systems modeled by equation (1.1), the minimal wave speed c * coincides with the spreading speed. Therefore, it is important to study the effects caused by the delay and other parameters (depending on specific models) on c * , cf.…”

“…Therefore, it is important to study the effects caused by the delay and other parameters (depending on specific models) on c * , cf. [3,5,6,8,9]. Another aspect of the problem concerns easily calculable upper and lower bounds for c * .…”

Глобальная Устойчивость Фронтов Бегущих Волн Для Нелокального Уравнения Диффузии С Запаздыванием

“…Они доказали теоремы существования и сравнения для решений квазимонотонных биустойчивых уравнений реакции-диффузии с дискретным запаздыванием и получили устойчивость фронтов бегущих волн с помощью элементарных методов сравнения суб-и суперрешений и методов просачивания, развитых в [3] (об этой технике см. также [11]- [13]). …”

Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity

“…There has been significant progress in the study of traveling wave solutions for both bistable and monostable equations; see, for example, Ai [1], Ashwin et al [2], Billingham [4], Faria et al [14,15], Gourley and Kuang [17,18], Liang and Wu [25], Ou and Wu [29], Ruan and Xiao [35], Wang et al [41,43], Wu and Zou [46], Zou [48], and the references cites therein.…”

“…Our method is similar to that of Carr and Chmaj [6] which has been used by Wang et al [43] (see also Diekmann and Kaper [11]). We first provide a technical lemma about the asymptotic behavior of a positive decreasing function, which is given by Carr and Chmaj [6,Proposition 2.3] and is important to prove our results.…”