具時間延遲合作型Lotka-Volterra系統之行進波解

Abstract

我們從參考書目[5]及參考書目[6]之定理2.1中得知： 當時間延遲夠小且定理2.1中所有的條件皆符合時， 利用上下解的技巧及單調疊代的方法可求出， 具時間延遲合作型Lotka-Volterra系統具有行進波解。 而現在我們希望可以找出較小的上解及降低對時間延遲的限制。 關鍵字：行進波解；上解；下解；時間延遲。

The existence of traveling wave front solution is established for diffusive and cooperative Lotka-Volterra system with time delays. The approaches used in this paper are the upper-lower solution technique, the monotone iteration by Wu and Zou in reference [6] for delayed reaction-diffusion systems. From the theorem 2.1 in reference [5] and theorem 4.5* in references [6], we know that if time delay is sufficiently small and all conditions in the above theorems hold. And then we have a traveling wave front solution. Now, we hope that we can change the upper and lower solutions in reference [5] and reduce the constraints on time delays. Keywords: Traveling wave solution; Upper solution; Lower solution;Time delay.