کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4610020 | 1338540 | 2015 | 34 صفحه PDF | دانلود رایگان |
In this paper we deal with the existence of traveling waves solutions (t.w.s.) for the reaction–diffusion equationut=uxx+f(u),ut=uxx+f(u), in a very general setting of reaction terms f with two distinguished stationary states, say 0 and 1. We link the existence of some type of solutions of the second order ODEu″+cu′+f(u)=0,u″+cu′+f(u)=0, with the existence of fast t.w.s. By defining fast solutions for this ODE, we find a value cM>0cM>0 related to the existence of global fast solutions and determine cMcM through a variational formula. Our results allow us particularly to show that any solution u(x,t)u(x,t) of the reaction–diffusion equation with compactly supported initial data and 0≤u(x,0)≤1,x∈R, satisfieslimt→+∞u(x+ct,t)=0, uniformly on compact sets, for all c , |c|>cM|c|>cM.Finally, we connect cMcM with the minimum speed of propagation of all t.w.s. c⁎c⁎.
Journal: Journal of Differential Equations - Volume 259, Issue 10, 15 November 2015, Pages 5406–5439